Process for the polymerization of 1-butene

; X whose; M whose; m whose A whose R and R are hydrocarbon machines among a formula (I) [type is a carbon atom, a germanium atom, or a silicon atom is 1 and 2 is the metal of four fellows of the periodic table of an element Hydrogen, A halogen atom or R, OR, OSOCF, OCOR, SR, NR, or PR (among a formula) ; whose substitution part R is a hydrocarbon machine -- L -- a formula (IIa) and (IIb) -- or (IIb) (among a formula) ; R, R, R whose T is oxygen (O), a sulfur atom (S), or CH basis, The bridge-like metallocene compound of] whose R, R, and R are hydrogen or a hydrocarbon machine; an organic aluminium compound with the catalyst system which can be contacted and obtained as arbitrarily as the compound; which can form one or more Al Mochi Sun or アルキル metallocene cations, The polymerization method of 1* butene which consists of a process which contacts 0*20-mol% of an alpha olefin to 1* butene under polymerization conditions arbitrarily.