Somewhere dense orbit of abelian subgroup of diffeomorphisms maps acting on Cn
Abstract
In this paper, we give a characterization for any abelian subgroup G of a lie group of diffeomorphisms maps of Cn, having a somewhere dense orbit G(x), x in Cn: G(x) is somewhere dense in Cn if and only if there are f1,....,f2n+1 in exp-1(G) such that f2n+1 in vect(f1,...,f2n) and Z.f1(x)+....+Z.f2n+1(x) is dense subgroup of Cn, where vect(f1,....,f2n) is the vector space over R generated by f1,....,f2n.
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