VISCOSITY MODIFIER FOR LUBRICATING OILS, ADDITIVE COMPOSITION FOR LUBRICATING OILS, AND LUBRICATING OIL COMPOSITION RELATEDAPPLICATION [0001] This application claims the priority benefits of U.S. provisional patent application 61/971,980, filed March 28, 2014, the entire contents of which are incorporated herein by reference. TECHNICAL FIELD [0002] The present invention relates to a viscosity modifier for lubricating oils, an additive composition for lubricating oils, and a lubricating oil composition. BACKGROUND ART [0003] Petroleum products have so-called temperature dependence of viscosity wherein a large variation in viscosity is exhibited with variation in temperature. For example, for lubricating oil compositions used for automobiles or the like, it is preferable that the temperature dependence of viscosity is small. Therefore, in order to decrease the temperature dependence of viscosity, a certain kind of polymer which is soluble in a lubricating oil base is used in lubricating oil as a viscosity modifier. [0004] Ethylene-a-olefin copolymers are widely used as viscosity modifiers for lubricating oils, and various improvements have been made in order to further improve the balance of performances of the lubricating oils (for example, see patent Document 1). [0005] In recent years, in view of the reduction of petroleum resources and environmental problems such as global warming, an improvement of fuel efficiency of automobiles which is aimed at reducing exhaust gas pollutants and CO2 emissions is required. Lowering of fuel consumption by lubricating oils is expected as a significant technology for lowering fuel consumption because of having excellent cost-effectiveness as compared to physical modification of the lubricated machinery, and the requirement for improving fuel efficiency by lubricating oils is growing. [0006] The power loss in an engine or transmission is divided into friction loss at a sliding part and agitation loss due to the viscosity of lubricating oil. In particular, reduction of viscosity resistance is one measure of lowering fuel consumption by engine oils. In recent years, fuel consumption is tested based on performance under conditions of comparatively low temperatures as well as that under conventional conditions of high temperatures, and thus reduction of viscosity resistance in a wide temperature range from low temperature to high temperature is desirable for improving fuel efficiency. [0007] Lowering viscosity is effective for the reduction of viscosity resistance of an engine oil. In particular, at a low temperature, reducing viscosity is effective for the reduction of both friction loss and agitation loss. However, this does not mean that the viscosity should be simply lowered, because abrasion is caused at a sliding part at a high temperature. In other words, it is desired that the viscosity is lowered as much as possible in order to reduce agitation loss at a non-sliding part while a certain minimum required viscosity is ensured to avoid abrasion at a sliding part. [0008] In order to reduce low-temperature viscosity, it is known to use a polymer as described in Patent Document 1, wherein the polymer dissolves in base oil and provides excellent thickening properties at a high temperature, while the solubility of the polymer in oil is decreased at a low temperature, and thereby its effective volume (flow volume) and impact on viscosity are decreased. [0009] Also, a viscosity modifier for lubricating oils comprising an ethylene/a-olefin copolymer containing a structural unit derived from ethylene and a structural unit derived from two or more kinds of a-olefins is known (for example, see Patent Document 2). [0010] The viscosity modifiers described in Patent Literatures 1 to 3 cause reduction in the low-temperature viscosity of a lubricating oil composition containing each of said modifiers and make a certain contribution to improvement of fuel efficiency under the condition of a low temperature in an engine (for examples, at the time of starting the engine). However, lowering of fuel consumption is increasingly required, and further reduction of low-temperature viscosity is thus demanded. Although improvement of fuel efficiency under the condition of a high temperature in an engine is also demanded, and high-temperature viscosity is increasingly reduced by lowering the viscosity of base oil, it is inferred that there is a limit to reduction in viscosity from the viewpoint of prevention of abrasion. In such circumstances, a viscosity modifier capable of reducing viscosity in good balance in a wide temperature range from low temperature to high temperature is demanded. [001 1] Since the additive compositions for lubricating oils described in Patent Documents 1 and 2 often have high viscosity, an improvement of fluidity in a wide temperature range from low temperature to high temperature is demanded from the viewpoint of an improvement of the efficiency of workability and transportability as well as reduction of the energy consumption of production facilities. CITATION LIST PATENTDOCUMENTS [0012] [Patent Document 1] International Publication WO 2000/034420 [Patent Document 2] International Publication WO 2006/028169 [Patent Document 3] International Publication WO 201 1/03833 1 SUMMARY OF THE INVENTION PROBLEMS TO BE SOLVED BY THE INVENTION [0013] It is an object of the present invention to provide a viscosity modifier for lubricating oils for obtaining an additive composition for lubricating oils having excellent fluidity in a wide temperature range from low temperature to high temperature. Further, it is an object of the present invention to provide a viscosity modifier for lubricating oils for obtaining a lubricating oil composition capable of reducing viscosity in good balance in a wide temperature range from low temperature to high temperature. [0014] It is an object of the present invention to provide an additive composition for lubricating oils having excellent fluidity in a wide temperature range from low temperature to high temperature. It is an object of the present invention to provide a lubricating oil composition capable of reducing viscosity in good balance in a wide temperature range from low temperature to high temperature. MEANS FOR SOLVING THE PROBLEMS [0015] As a result of intensive investigation, the present inventors found that an additive composition for lubricating oils having excellent fluidity in a wide temperature range from low temperature to high temperature as compared to a conventional additive composition for lubricating oils is obtained by using a viscosity modifier for lubricating oils containing a specific ethylene-a-olefin copolymer in an additive composition for lubricating oils. Further, it was found that a lubricating oil composition capable of reducing viscosity in good balance in a wide temperature range from low temperature to high temperature as compared to a conventional lubricating oil composition is obtained by using a viscosity modifier for lubricating oils containing a specific ethylene- a-olefin copolymer in a lubricating oil composition. [0016] The viscosity modifier for lubricating oils of the present invention comprises an ethylene- a-olefin copolymer (A) which comprises 30 to 50 mole% of structural units derived from at least one a-olefin selected from a-olefins having 4 and 5 carbon atoms and 50 to 70 mole% of structural units derived from ethylene with the proviso that the total of all structural units of said copolymer is 100 mole% and which satisfies the following requirements (a), (b), and (c): [0017] (a): A glass transition temperature (Tg) as measured by differential scanning calorimetry (DSC) is in a range of -75 to -65°C. (b): A melting point (Tm) as measured by differential scanning calorimetry (DSC) is not substantially observed or is not a melting point (Tm) of -25°C or more. (c): Intrinsic viscosity [h] as measured in a decalin solvent at 135°C is 1.0 to 2.8 dl/g. [001 8] The weight average molecular weight of the ethylene- a-olefin copolymer (A) is preferably 100,000 to 400,000 as measured by gel permeation chromatography (GPC). [0019] The ethylene- a-olefin copolymer preferably comprises 1-butene as a structural unit. An additive composition for lubricating oils of the present invention comprises the viscosity modifier for lubricating oils and an oil (B) and comprises the ethylene- a-olefin copolymer (A) and said oil (B) at a weight ratio (A)/(B) of 1/99 to 50/50. [0020] A lubricating oil composition of the present invention comprises the viscosity modifier for lubricating oils and a lubricating oil base (BB), and the ethylene- a-olefin copolymer (A) in an amount of 0.1 to 5% by weight is contained in 100% by weight of said lubricating oil composition. [0021] It is preferable that in the lubricating oil composition of the present invention, 0.05 to 5% by weight of a pour-point depressant (C) is further contained in 100% by weight of said lubricating oil composition. EFFECT OF THE INVENTION [0022] An additive composition for lubricating oils having excellent fluidity in a wide temperature range from low temperature to high temperature can be obtained by using the viscosity modifier for lubricating oils of the present invention. Further, a lubricating oil composition with reduced viscosity in good balance in a wide temperature range from low temperature to high temperature, as compared to conventional one, can be obtained by using the viscosity modifier for lubricating oils of the present invention. [0023] The additive composition for lubricating oils of the present invention has excellent fluidity in a wide temperature range from low temperature to high temperature, as compared to a conventional additive composition for lubricating oils. Further, the lubricating oil composition of the present invention results in reduction of viscosity in good balance in a wide temperature range from low temperature to high temperature, as compared to a conventional lubricating oil composition. BRIEF DESCRIPTION OF THE DRAWINGS [0024] Figure 1 is a plot of MRV of a composition, determined by extrapolation or interpolation from three measurement data, with the proviso that HTHS viscosity is 2.9 mPa-s, versus SSI (shear stability index) determined in the same manner. Figure 2 is a plot of kinematic viscosity (KV) at 100°C of a composition, determined by extrapolation or interpolation from three measurement data, with the proviso that HTHS viscosity is 2.9 mPa-s, versus SSI determined in the same manner. Figure 3 is a plot of pour point of a polymer solution having a concentration of 10% by weight in a PAO-4 solvent, as a function of SSI of a composition, determined by extrapolation or interpolation from three measurement data, with the proviso that HTHS viscosity is 2.9 mPa-s. Figure 4 is a plot of kinematic viscosity at 100°C of a polymer solution having a concentration of 10% by weight in a PAO-4 solvent, as a function of SSI of a composition, determined by extrapolation or interpolation from three measurement data, with the proviso that HTHS viscosity is 2.9 mPa-s. Figure 5 is a plot of MRV of a composition, determined by extrapolation or interpolation from three measurement data, with the proviso that HTHS viscosity is 2.9 mPa-s, versus SSI determined in the same manner. DESCRIPTION OF EMBODIMENTS [0025] In the following, the present invention will be specifically explained. [Viscosity Modifier for Lubricating Oils] [Ethylene- a-Olefin Copolymer (A)] (Monomer Component, Mole Fraction) The viscosity modifier for lubricating oils of the present invention comprises an ethylene- a-olefin copolymer (A) which comprises ethylene and at least one a-olefin selected from a-olefins having 4 and 5 carbon atoms as structural units. [0026] Said ethylene- -olefin copolymer (A) generally contains 30 to 50 mole% of structural units derived from at least one a-olefin selected from a-olefins having 4 and 5 carbon atoms and generally contains 50 to 70 mole% of structural units derived from ethylene, with the proviso that the total of all structural units of said copolymer is 100 mole%. The upper limit of the structural unit derived from ethylene is preferably 69 mole%, further preferably 68 mole%, further more preferably 65 mole%, particularly preferably 64 mole%, while the lower limit thereof is preferably 52 mole%, further preferably 55 mole%, particularly preferably 59 mole%. Further, the upper limit of said a-olefin is preferably 48 mole%, further preferably 45 mole%, particularly preferably 4 1 mole%, while the lower limit thereof is preferably 31 mole%, further preferably 32 mole%, further more preferably 35 mole%, particularly preferably 36 mole%. A content of said a-olefin of less than 30 mole% results in no suitability as a viscosity modifier for lubricating oils since, in particular, fluidity at low temperature is deteriorated and viscosity at low temperature is not reduced. A content of said a-olefin of more than 50 mole% results in no suitability as a viscosity modifier for lubricating oils since shear stability is deteriorated. The molar ratio between the structural units derived from ethylene and the structural units derived from at least one a-olefin selected from a-olefins having 4 and 5 carbon atoms can fall within the above-mentioned ranges by controlling ratios between raw material monomers. [0027] The lubricating oil additive composition comprising said copolymer (A) has excellent fluidity in a wide temperature range from low temperature to high temperature, as compared to a conventional lubricating oil additive composition. Further, the lubricating oil composition comprising said copolymer (A) results in reduction of viscosity in good balance in a wide temperature range from low temperature to high temperature, as compared to a conventional lubricating oil composition. [0028] The structural unit derived from ethylene in said copolymer (A) can be measured by 1 C-NMR according to a method described in Macromolecule Analysis Handbook, ed. Research Committee of Polymer Analysis, The Japan Society for Analytical Chemistry (Kinokuniya Company Ltd., January 12, 1995). [0029] Examples of said a-olefins having 4 or 5 carbon atoms include 1-butene, 1-pentene, 3-methyl- 1-butene, and the like. In particular, 1-butene is preferred in terms of shear stability. The a-olefins may be used singly or in combination of two or more kinds. [0030] As said copolymer (A), ethylene-butene- 1 random copolymer, ethylene-pentene- 1 random copolymer, ethylene-3-methyl- 1-butene random copolymer, ethylene-butene- 1-pentene- 1 random terpolymer, ethylene-butene- 1-3 -methyl- 1-butene random terpolymer, and ethylene-3-methyl- 1-butene-pentene-l random terpolymer are preferred, ethylene-butene- 1 random copolymer, ethylene-pentene- 1 random copolymer, and ethylene-3-methyl- 1-butene random copolymer are more preferred, and ethylene-butene- 1 random copolymer is particularly preferred, in terms of shear stability. [003 1] As the conventional viscosity modifier for lubricating oils, a copolymer such as ethylene propylene rubber (EPR) has been used. However, in accordance with the present invention, said ethylene-a-olefin copolymer (A) comprising the structural unit derived from ethylene and the structural unit derived from a-olefins having 4 and/or 5 carbon atoms in specific amounts is used as the viscosity modifier for lubricating oils. The lubricating oil composition comprising said copolymer (A) results in reduction of viscosity in good balance in a wide temperature range from low temperature to high temperature, as compared to a conventional lubricating oil composition. Further, the additive composition for lubricating oils comprising said copolymer (A) has excellent fluidity in a wide temperature range from low temperature to high temperature, as compared to a conventional additive composition for lubricating oils. [0032] The present inventors infer that if side chains derived from a comonomer in said ethylene- a-olefin copolymer are short, the molecular chains of the ethylene- a-olefin copolymer are expanded in a base oil, leading to viscosity increase, and that if the number of the side chains is too small, crystallization occurs or the action of a pour-point depressant is inhibited to result in poor fluidity at low temperature. The present inventors infer that too long side chains or too large number of side chains, on the other hand, result in poor shear stability and unsuitability as the viscosity modifier for lubricating oils. The present inventors infer that the use of said ethylene- a-olefin copolymer comprising a-olefins having 4 and/or 5 carbon atoms in specific amounts rather than propylene or a comonomer having a long side chain, conventionally used as a comonomer, results in reduction of viscosity and in excellence in fluidity, in good balance in a wide temperature range from low temperature to high temperature. Accordingly, it is preferable that the ethylene- -olefin copolymer of the present invention contains the contents of ethylene and said a-olefins and has a side chain having 2 to 3 carbon atoms. [0033] (Tg) The glass transition temperature (Tg) of said ethylene- a-olefin copolymer (A), measured by differential scanning calorimetry (DSC), is generally in a range of -75 to -65°C, preferably in a range of -73 to -67°C. The lubricating oil composition comprising said copolymer (A) is preferred because of resulting in reduction of viscosity in good balance in a wide temperature range from low temperature to high temperature, as compared to a conventional lubricating oil composition. Further, the additive composition for lubricating oils comprising said copolymer (A) is preferred because of having excellent fluidity in a wide temperature range from low temperature to high temperature, as compared to a conventional additive composition for lubricating oils. The glass transition temperature (Tg) deviating from said range results in unsuitability as the viscosity modifier for lubricating oils since, in particular, fluidity at low temperature is deteriorated and reduction of viscosity at low temperature cannot be achieved. The glass transition temperature (Tg) can be controlled, for example, by increasing or decreasing an amount of the ethylene monomer to be fed. The glass transition temperature (Tg), which is controlled by various factors, tends to be increased when the melting point (Tm) as measured by differential scanning calorimetry (DSC) is increased to a certain degree. [0034] In the present invention, the glass transition temperature (Tg) of said copolymer (A) by differential scanning calorimetry (DSC) is measured as follows (al): (al) The following method is conducted using a differential scanning calorimeter (RDC220) manufactured by SEIKO, calibrated with an indium standard. [0035] A sample pan is placed on DSC cell, and the DSC cell is heated from 30°C (room temperature) to 150°C at 10°C/min under nitrogen atmosphere, then held at 150°C for 5 minutes, and thereafter cooled to -100°C at 10°C/min (cooling process). The intersection point of the tangent line on the inflection point (the point on which an upward convex curve turns into a downward convex curve) of the enthalpy curve obtained in the cooling process is regarded as the glass transition temperature (Tg). [0036] (Tm) Said ethylene- a-olefin copolymer (A) has a substantially unobserved melting point (Tm) measured by differential scanning calorimetry (DSC) or does not have a melting point (Tm) of -25°C or more. As used herein, the substantially unobserved melting point refers to a situation in which a heat of fusion DH (Tm) (unit: J/g) measured by differential scanning calorimetry (DSC) is not substantially observed. The situation in which the heat of fusion DH (Tm) is not substantially observed refers to a situation in which no peak is observed by DSC measurement. Said copolymer (A) that has a substantially unobserved melting point (Tm) or does not have a melting point of -25°C or more means that it is amorphous at room temperature. The lubricating oil composition comprising said copolymer (A) is preferred because of resulting in reduction of viscosity in good balance in a wide temperature range from low temperature to high temperature, as compared to a conventional lubricating oil composition. Further, the additive composition for lubricating oils comprising said copolymer (A) is preferred because of having excellent fluidity in a wide temperature range from low temperature to high temperature as compared to a conventional additive composition for lubricating oils. [0037] The lubricating oil additive composition comprising the copolymer (A) having a substantially unobserved melting point (Tm) is preferred because of having excellent fluidity at low temperature as compared to a conventional lubricating oil additive composition. The lubricating oil composition comprising the copolymer (A) having a substantially unobserved melting point (Tm) is preferred because of having excellent fluidity at low temperature. [003 8] The copolymer (A) having a melting point of -25°C or more results in unsuitability as the viscosity modifier for lubricating oils since, in particular, fluidity at low temperature is deteriorated and reduction of viscosity at low temperature cannot be achieved. The melting point (Tm) can be controlled, for example, by increasing or decreasing an amount of the ethylene monomer to be fed. In the present invention, increase in an amount of the ethylene monomer leads to increase in the melting point (Tm), whereas decrease in an amount of the ethylene monomer leads to decrease in the melting point (Tm) or no observation of the melting point (Tm). The melting point (Tm) of said copolymer (A) by differential scanning calorimetry (DSC) is measured as follows (a2): (a2) The following method is conducted using a differential scanning calorimeter (RDC220) manufactured by SEIKO Corporation, calibrated with an indium standard. [0039] A sample pan is placed on DSC cell, and the DSC cell is heated from 30°C (room temperature) to 150°C at 10°C/min under nitrogen atmosphere. Then, the DSC cell is held at 150°C for 5 minutes, thereafter cooled to -100°C at 10°C/min, held at -100°C for 5 minutes, and thereafter heated to 150°C at 10°C/min (2nd heating process). The fusion peak top temperature of the enthalpy curve obtained from the 2nd heating process is regarded as a melting point (Tm). If there are two or more fusion peaks, the one having the highest peak is defined as Tm. [0040] ([h]) The intrinsic viscosity [h] of said ethylene- a-olefin copolymer (A), measured in a decalin solvent at 135°C, is generally 1.0 to 2.8 dl/g, preferably 1.0 to 2.5 dl/g, further preferably 1.0 to 2.2 dl/g. The intrinsic viscosity [h] can fall within the above-mentioned ranges by controlling polymerization temperature at the time of polymerization, a molecular weight regulator, e.g., hydrogen, or the like. [0041] The lubricating oil composition comprising said copolymer (A) is preferred because of resulting in reduction of viscosity in good balance in a wide temperature range from low temperature to high temperature, as compared to a conventional lubricating oil composition, while having shear stability useful for the viscosity modifier for lubricating oils. Further, the additive composition for lubricating oils comprising said copolymer (A) is preferred because of having excellent fluidity in a wide temperature range from low temperature to high temperature, as compared to a conventional additive composition for lubricating oils, while having shear stability useful for the viscosity modifier for lubricating oils. The intrinsic viscosity deviating from said range results in deterioration of shear stability and in unsuitability of as the viscosity modifier for lubricating oils. [0042] (Density) The density of said ethylene- a-olefin copolymer (A) is not particularly limited as long as exerting the effects of the present invention. The density is preferably in a range of 858 to 865 kg/m . The lubricating oil composition comprising said copolymer (A) is preferred because of resulting in reduction of viscosity in good balance in a wide temperature range from low temperature to high temperature, as compared to a conventional lubricating oil composition. Further, the additive composition for lubricating oils comprising said copolymer (A) is preferred because of having excellent fluidity in a wide temperature range from low temperature to high temperature, as compared to a conventional additive composition for lubricating oils. [0043] (Mw, Mw/Mn) The weight average molecular weight (Mw) of said ethylene- a-olefin copolymer (A) measured by gel permeation chromatography (GPC) is not particularly limited as long as exerting the effects of the present invention. The weight average molecular weight (Mw) is preferably 100,000 to 400,000, more preferably 120,000 to 350,000, still more preferably 140,000 to 350,000, particularly preferably 140,000 to 330,000 in terms of shear stability. The term "weight average molecular weight" as used herein refers to a weight average molecular weight in terms of polystyrene measured by GPC. [0044] The weight average molecular weight (Mw) can fall within the above-mentioned ranges by controlling, for example, polymerization temperature at the time of polymerization, a molecular weight regulator, e.g., hydrogen, or the like. The lubricating oil composition comprising said copolymer (A) is preferred because of resulting in reduction of viscosity in good balance in a wide temperature range from low temperature to high temperature, as compared to a conventional lubricating oil composition. Further, the additive composition for lubricating oils comprising said copolymer (A) is preferred because of having excellent fluidity in a wide temperature range from low temperature to high temperature, as compared to a conventional additive composition for lubricating oils. [0045] The ratio (molecular weight distribution, Mw/Mn, in terms of polystyrene) of the weight average molecular weight (Mw) to number average molecular weight (Mn) of said copolymer (A) as measured by GPC is not particularly limited as long as exerting the effects of the present invention. The ratio is preferably 4.0 or less, more preferably 3.0 or less, further preferably 2.5 or less. The lower limit of the molecular weight distribution is not particularly limited as long as exerting the effects of the present invention. The lower limit is generally 1.0. [0046] In the present invention, the reason why the lubricating oil composition comprising said ethylene- -olefin copolymer (A) has excellent viscosity characteristics in a wide temperature range from low temperature to high temperature is unknown. However, the present inventors infer that in a lubricating oil composition at low temperature, said copolymer (A) forms an aggregate in a specific amount of the oil (B) and thereby its flow volume (effective volume) is reduced, and as a result thereof the lubricating oil composition has excellent viscosity characteristics particularly at low temperature. Further, since the aggregate is not precipitated or does not otherwise come out in the lubricating oil composition, the lubricating oil composition also has excellent low-temperature storage property. It is considered that in a lubricating oil composition at high temperature, the ethylene-a-olefin copolymer (A) has, in a specific amount of base oil, high solubility in said base oil, and its aggregate size is small. If the aggregate size is small, a reduction in viscosity due to deformation of the aggregate is also lowered, for example, when the lubricating oil composition comprising said copolymer (A) receives large shear between sliding parts. Therefore, a temporary reduction in viscosity under shearing is lowered. In other words, it is considered that since said copolymer (A) reduces an energy loss while keeping the minimum high temperature high shear (HTHS) viscosity necessary from the viewpoint of abrasion resistance, viscosity can be reduced at parts ranging from a non-sliding part and a low shear region to a high shear region. From such a viewpoint, the present inventors infer that the lubricating oil composition comprising the ethylene- a-olefin copolymer (A) according to the present invention has excellent viscosity characteristics in a wide temperature range from low temperature to high temperature. [0047] Further, the reason why the additive composition for lubricating oils comprising said ethylene- a-olefin copolymer (A) has excellent fluidity in a wide temperature range from a low temperature to a high temperature is unknown. However, the present inventors infer that when a specific amount of said copolymer (A) is used in the additive composition for lubricating oils, since the stretching of molecular chains of said copolymer (A) in a base oil is small as compared to a conventional viscosity modifier, its flow volume (effective volume) is reduced, and thereby the additive composition for lubricating oils has excellent fluidity. [0048] (Method for Producing Ethylene-a-Olefin Copolymer (A)) The ethylene- a-olefin copolymer (A) according to the present invention can be produced by copolymerizing ethylene, an a-olefin, and, if necessary, another monomer in the presence of a known olefin polymerization catalyst. As the known olefin polymerization catalyst, a metallocene-based catalyst, a solid titanium catalyst, a vanadium catalyst, or the like is used. In particular, the metallocene-based catalyst is preferred, in which particularly preferred is a metallocene-based catalyst comprising a metallocene compound of a transition metal selected from e.g., Group 4 of the periodic table, an organoaluminum oxy-compound and/or an ionized ionic compound capable of reacting with the transition metal metallocene compound to form an ion. Particularly preferred in terms of composition distribution is a combination of the transition metal metallocene compound and the ionized ionic compound capable of reacting with the transition metal metallocene compound to form an ion. [0049] Olefin Polymerization Catalyst In the following, each catalyst will be explained. Further, in the present invention, reference to a catalyst described in Japanese Patent Laid-Open No. 2003-105365 can be made as a catalyst for an olefin copolymer. [0050] (1) Metallocene-Based Catalyst A known catalyst can be used as a metallocene compound of a transition metal selected from Group 4 of the periodic table that forms a metallocene-based catalyst. The metallocene compound is specifically represented by the following general formula (i): MLx (i) In the formula (i), M is a transition metal selected from Group 4 of the periodic table, specifically zirconium, titanium, or hafnium, and x is the valence of the transition metal. [005 1] L is a ligand coordinating to a transition metal. Of such ligands, at least one ligand L is a ligand having a cyclopentadienyl skeleton. The ligand having a cyclopentadienyl skeleton may have a substituent. [0052] Examples of the ligand having a cyclopentadienyl skeleton include cyclopentadienyl group; indenyl group; 4,5,6,7-tetrahydroindenyl group; fluorenyl group; and the like. These groups may be substituted with hydrocarbon group having the total number of carbon atoms of 1 to 20, or silicon-containing group having the total number of carbon atoms of 1 to 20. In the case where 2 or more are substituted, these substituents may be each identical or different. Further, the hydrocarbon groups having the total number of carbon atoms of 1 to 20 refer to alkyl, alkenyl, alkynyl and aryl groups that are composed of carbon and hydrogen only. Among them, those in which neighboring hydrogen atoms are both substituted to form alicyclic group or aromatic group are included. The hydrocarbon groups having the total number of carbon atoms of 1 to 20 include, in addition to alkyl, alkenyl, alkynyl and aryl groups that are composed of carbon and hydrogen only, heteroatom-containing hydrocarbon groups in which a part of hydrogen atoms directly bonded to these carbon atoms are substituted with halogen atom, oxygen-containing group, nitrogen-containing group, or silicon-containing group, or groups in which neighboring hydrogen atoms form alicyclic group. Specific examples of the hydrocarbon groups having the total number of carbon atoms of 1 to 20 include straight-chain hydrocarbon groups such as methyl group, ethyl group, n-propyl group, allyl group, n-butyl group, n-pentyl group, n-hexyl group, n-heptyl group, n-octyl group, n-nonyl group, n-decanyl group and the like; branched-chain hydrocarbon groups such as isopropyl group, t-butyl group, amyl group, 3-methylpentyl group, 1,1-diethylpropyl group, 1,1-dimethylbutyl group, 1-methyl- 1-propylbutyl group, 1,1-propylbutyl group, l,l-dimethyl-2-methylpropyl group, 1-methyl- l-isopropyl-2-methylpropyl group and the like; cyclic saturated hydrocarbon groups such as cyclopentyl group, cyclohexyl group, cycloheptyl group, cyclooctyl group, norbornyl group, adamantyl group and the like; cyclic unsaturated hydrocarbon groups such as phenyl group, naphthyl group, biphenyl group, phenanthryl group, anthracenyl group and the like, and those in which the aromatic ring is substituted with alkyl groups; saturated hydrocarbon groups that are substituted with aryl-group such as benzyl group, cumyl group and the like; and heteroatom-containing hydrocarbon groups such as methoxy group, ethoxy group, phenoxy group, N-methylamino group, trifluoromethyl group, tribromomethyl group, pentafluoroethyl group, pentafluorophenyl group and the like. The silicon-containing groups refer, for example, to groups in which the ring-carbon of cyclopentadienyl group is directly bonded with a covalent bond to silicon atom, and specifically to alkylsilyl groups and arylsilyl groups. Examples of the silicon-containing groups having the total number of carbon atoms of 1 to 20 include trimethylsilyl group, triphenylsilyl group and the like. [0053] When the compound represented by the general formula (i) has two or more groups having a cyclopentadienyl skeleton as the ligands L, two groups having a cyclopentadienyl skeleton of them may be bonded to each other through an alkylene group such as ethylene or propylene, a substituted alkylene group such as isopropylidene or diphenylmethylene, di-p-tolylmethylene, bis[4-(dimethylamino)phenyl]methylene, bis(4-methoxy-3-methylphenyl)methylene, a silylene group, a substituted silylene group such as dimethylsilylene, diphenylsilylene, or methylphenylsilylene, or the like. [0054] Examples of L other than the ligand having a cyclopentadienyl skeleton include hydrocarbon groups having 1 to 12 carbon atoms, alkoxy groups, aryloxy groups, halogen atoms, a hydrogen atom, sulfonic acid-containing groups (-S0 R ) (wherein R is an alkyl group, an alkyl group substituted with a halogen atom, an aryl group, or an aryl group substituted with a halogen atom or an alkyl group), and the like. [0055] Examples of the hydrocarbon groups having 1 to 12 carbon atoms include alkyl groups, cycloalkyl groups, aryl groups, aralkyl groups, and the like, and more specifically include alkyl groups such as methyl, ethyl, n-propyl, isopropyl, n-butyl, isobutyl, sec-butyl, t-butyl, pentyl, hexyl, octyl, decyl, and dodecyl; cycloalkyl groups such as cyclopentyl and cyclohexyl; aryl groups such as phenyl and tolyl; and aralkyl groups such as benzyl and neophyl. [0056] Examples of the alkoxy groups include methoxy, ethoxy, n-propoxy, isopropoxy, n-butoxy, isobutoxy, sec-butoxy, t-butoxy, pentoxy, hexoxy, octoxy, and the like. [0057] Examples of the aryloxy groups include phenoxy and the like. Examples of the sulfonic acid-containing groups (-S0 R ) include methanesulfonato, p-toluenesulfonato, trifluoromethanesulfonato, p-chlorobenzenesulfonato, and the like. [0058] Examples of the halogen atoms include fluorine, chlorine, bromine, and iodine. Listed below are examples of the metallocene compounds containing at least two ligands having a cyclopentadienyl skeleton: [0059] bis(methylcyclopentadienyl)zirconium dichloride; bis(ethylcyclopentadienyl)zirconium dichloride; bis(n-propylcyclopentadienyl)zirconium dichloride; bis(indenyl)zirconium dichloride; bis(4,5,6,7-tetrahydroindenyl)zirconium dichloride; di-p-tolylmethylene(cyclopentadienyl)(octamethyloctahydridodibenzfluorenyl)zirc onium dichloride; [bis[4-(dimethylamino)phenyl]methylene( h -cyclopentadienyl)( h -octamethylocta hydrodibenzofluorenyl)]hafnium dichloride; [bis(4-methoxy-3-methylphenyl)methylene( h -cyclopentadienyl)( h -octamethyloctahydrod ibenzofluorenyl)]hafnium dichloride; and the like. [0060] Also mentions can be made of compounds in which a zirconium metal is replaced with a titanium or hafnium metal, or compounds in which a hafnium metal is replaced with a titanium or zirconium metal in such compounds as described above. In accordance with the present invention, as a metallocene compound, a compound represented by the following general formula (ii) is also employable. lM lX z (ii) (wherein M is a metal of Group 4 of the periodic table or a metal of lanthanide series; L1 is a derivative of derealization p bond group and imparts restraint geometrical shape to a metal M1 active site; X is each independently hydrogen, halogen, a hydrocarbon group containing 20 or less carbon atoms, silicon, or germanium, a silyl group, or a germyl group). [0061] Of the compounds represented by the general formula (ii), preferable are compounds represented by the following general formula (iii). [0062] In the formula, M1 is titanium, zirconium, or hafnium, and X is the same as described above. Cp is p-bonded to M1 and is a substituted cyclopentadienyl group having a substituent Z. Z is oxygen, sulfur, boron, or an element of Group 14 of the periodic table (for example, silicon, germanium, or tin), Y is a ligand containing nitrogen, phosphorus, oxygen, or sulfur, and Z and Y may together form a condensed ring. [0063] Specific examples of the compounds represented the general formula (iii) include [dimethyl(t-butylamide)(tetramethyl- h -cyclopentadienyl)silane]titanium dichloride, [(t-butylamide)(tetramethyl- | -cyclopentadienyl)- 1,2-ethanediyl]titanium dichloride, [dibenzyl(t-butylamide)(tetramethyl- h -cyclopentadienyl)silane]titanium dichloride, [dimethyl(t-butylamide)(tetramethyl- h -cyclopentadienyl)silane]dibenzyltitanium, [dimethyl(t-butyl amide)(tetramethyl- h -cyclopentadienyl)silane]dimethyltitanium, [(t-butylamide)(tetramethyl- h -cyclopentadienyl)-l,2-ethanediyl]dibenzyltitanium, [(methylamide)(tetramethyl- h -cyclopentadienyl)-l,2-ethanediyl]dineopentyltitanium, [(phenylphosphide)(tetramethyl- h -cyclopentadienyl)methylene]diphenyltitanium, [dibenzyl(t-butylamide)(tetramethyl- h -cyclopentadienyl)silane]dibenzyltitanium, [dimethyl(benzylamide)( h -cyclopentadienyl]silane]di(trimethylsilyl)titanium, [dimethyl(phenylphosphide)(tetramethyl- h -cyclopentadienyl)silane]dibenzyltitanium, [(tetramethyl-h -cyclopentadienyl)-l,2-ethanediyl]dibenzyltitanium, [2-h -(tetramethyl-cyclopentadienyl)-l-methyl-ethanolate(2-)]dibenzyltitanium, [2-h -(tetramethyl-cyclopentadienyl)-l-methyl-ethanolate(2-)]dimethyltitanium, [2-((4 ,^,8 ,9,9 -h)-9H -ίΊ o h-9 1 1o1 ho1 ί ( -)] 1ί ί h i , [2-((4a,4b,8a,9,9a-h)-9H-fluoren-9-yl)cyclohexanolate(2-)]dibenzyltitanium, and the like. [0064] Also mentions can be made of compounds in which a titanium metal is replaced with a zirconium or hafnium metal in such compounds as described above. These metallocene compounds may be used singly or in combination of two or more kinds. [0065] In accordance with the present invention, a zirconocene compound having zirconium as the central metal atom and at least two ligands having a cyclopentadienyl skeleton and a hafnocene compound having hafnium as the central metal atom and at least two ligands having a cyclopentadienyl skeleton are preferably used as the metallocene compound represented by the general formula (i). Further, the metallocene compound represented by the general formula (ii) or (iii) preferably has titanium as the central metal atom. [0066] Cocatalyst As an organoaluminum oxy-compound that forms a metallocene-based catalyst, aluminoxane known in the art can be used. The organoaluminum oxy-compound may also be a benzene-insoluble organoaluminum oxy-compound. Specifically, the organoaluminum oxy-compound is represented by the following general formula. [0067] R A ( O —A \ .— A R - Ci v) R (In the above general formulae (iv) and (v), R is a hydrocarbon group such as methyl, ethyl, propyl, or butyl, preferably methyl or ethyl, particularly preferably methyl, m is an integer of 2 or more, preferably 5 to 40). The aluminoxane may be formed of an alkyloxy aluminum unit mixture including an alkyloxy aluminum unit represented by the formula (OA^R 1)) and an alkyloxy aluminum unit represented by the formula (OAl(R2)) [wherein examples of R1 and R2 may include a hydrocarbon group like R, and R1 and R2 represent groups different from each other]. [0068] Examples of ionized ionic compounds that form a metallocene-based catalyst may include Lewis acids, ionic compounds, and the like. Examples of the Lewis acids include compounds represented by BR (R is a phenyl group which may have a substituent such as fluorine, methyl, or trifluoromethyl, or fluorine). Examples thereof include trifluoroboron, triphenylboron, tris(4-fluorophenyl)boron, tris(3 ,5-difluorophenyl)boron, tris(4-fluoromethylphenyl)boron, tris(pentafluorophenyl)boron, tris(p-tolyl)boron, tris(o-tolyl)boron, tris(3,5-dimethylphenyl)boron, and the like. [0069] Examples of the ionic compounds may include trialkyl-substituted ammonium salts, N,N-dialkylanilinium salts, dialkylammonium salts, triarylphosphonium salts, and the like. Specific examples of the trialkyl-substituted ammonium salts include triethylammoniumtetra(phenyl)borate, tripropylammoniumtetra(phenyl)borate, tri(n-butyl)ammoniumtetra(phenyl)borate, trimethylammoniumtetra(p-tolyl)borate, trimethylammoniumtetra(o-tolyl)borate, tributylammoniumtetra(pentafluorophenyl)borate, tripropylammoniumtetra(o,p-dimethylphenyl)borate, tributylammoniumtetra(m,m-dimethylphenyl)borate, tributylammoniumtetra(p-trifluoromethylphenyl)borate, tri(n-butyl)ammoniumtetra(o-tolyl)borate, and the like. [0070] Examples of the N,N-dialkylanilinium salts include N,N-dimethylaniliniumtetra(phenyl)borate, N,N-diethylaniliniumtetra(phenyl)borate, N,N-2,4,6-pentamethylaniliniumtetra(phenyl)borate, and the like. [0071] Examples of the dialkylammonium salts include di( 1-propyl)ammoniumtetra(pentafluorophenyl)borate, dicyclohexylammoniumtetra(phenyl)borate, and the like. [0072] Examples of the triarylphosphonium salts include triphenylphosphoniumtetra(phenyl)borate, tri(dimethylphenyl)phosphoniumtetra(phenyl)borate, and the like. [0073] Furthermore, examples of the ionic compounds may also include triphenylcarbeniumtetrakis(pentafluorophenyl)borate, N,N-dimethylaniliniumtetrakis(pentafluorophenyl)borate, ferroceniumtetra(pentafluorophenyl)borate, and the like. [0074] In particular, the ionized ionic compounds are preferably used in view of controlling the composition distribution of the ethylene- a-olefin copolymer. When a metallocene-based catalyst is formed, an organoaluminum compound may also be used together with an organoaluminum oxy-compound and/or an ionized ionic compound. Examples of the organoaluminum compound include compounds represented by the following general formula (vi). In the formula, R1 is a hydrocarbon group having 1 to 15, preferably 1 to 4 carbon atoms, X is a halogen atom or a hydrogen atom, and n is 1 to 3. [0075] Examples of the hydrocarbon group having 1 to 15 carbon atoms include an alkyl group, a cycloalkyl group, or an aryl group. Specific examples thereof include methyl, ethyl, n-propyl, isopropyl, isobutyl, pentyl, hexyl, octyl, cyclopentyl, cyclohexyl, phenyl, tolyl, and the like. [0076] Specific examples of the organoaluminum compound include the following compounds: trialkylaluminium such as trimethylaluminum, triethylaluminium, triisopropylaluminum, triisobutylaluminium, trioctylaluminum, or tri-2-ethylhexylaluminum; alkenylaluminum such as isoprenylaluminum represented by the general formula: (i-C4H 9)xAly(C5Hio)z (wherein x, y, and z are positive numbers, and z³2x is satisfied); trialkenylaluminum such as triisopropenylaluminum; dialkylaluminum halides such as dimethylaluminum chloride, diethylaluminum chloride, diisopropylaluminum chloride, diisobutylaluminum chloride, and dimethylaluminum bromide; alkylaluminum sesquihalides such as methylaluminum sesquichloride, ethylaluminum sesquichloride, isopropylaluminum sesquichloride, butylaluminum sesquichloride, and ethylaluminum sesquibromide; alkylaluminum dihalides such as methylaluminum dichloride, ethylaluminum dichloride, isopropylaluminum dichloride, and ethylaluminum dibromide; dialkylaluminum hydrides such as diethylaluminum hydride and dibutylaluminum hydride; alkylaluminum dihydrides such as ethylaluminum dihydride and propylaluminum dihydride; and the like. [0077] The ethylene- a-olefin copolymer (A) according to the present invention can be obtained by generally copolymerizing monomers (ethylene, a-olefins having 4 and/or 5 carbon atoms, and, if necessary, another monomer) that form a copolymer in a liquid phase in the presence of such a metallocene-based catalyst as described above. In this case, a hydrocarbon solvent is generally used as a polymerization solvent, and an a-olefin such as 1-butene may also be used. [0078] (2) Solid Titanium-Based Catalyst As the solid titanium catalyst, for example, a solid titanium catalyst component formed by bringing (a) a titanium compound and (b) a magnesium compound represented by the formula: MgOR ORb [R and Rb represent an alkyl group or an aryl group, and R and Rb may be the same or different] into contact with (c) an electron donor is used without limitation. Examples of such catalysts include those described in [0059] line 6 to [0079] line 9 in Japanese Patent Laid-Open No. 2003-105365. [0079] (3) Vanadium-Based Catalyst The vanadium catalyst comprises (a) a soluble vanadium compound and (b) an organoaluminum compound. [0080] The soluble vanadium compound (v-1) that forms the vanadium-based catalyst (a) is specifically represented by the following general formula: VO(OR)aXb orV(OR) Xd wherein R represents a hydrocarbon group such as an alkyl group, a cycloalkyl group, or an aryl group, X represents a halogen atom, and a, b, c, and d each satisfy 0£a£3, 0£b£3, 2£a+b£3, 0£c£4, 0£d£4, and 3£c+d£4 (a described above preferably satisfies l