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Somewhere dense orbit of abelian subgroup of diffeomorphisms maps acting on C^n

Research paper by Yahya N'Dao, Adlene Ayadi

Indexed on: 07 Nov '12Published on: 07 Nov '12Published in: Mathematics - Dynamical Systems



Abstract

In this paper, we give a characterization for any abelian subgroup G of a lie group of diffeomorphisms maps of C^n, having a somewhere dense orbit G(x), x in C^n: G(x) is somewhere dense in C^n if and only if there are f_{1},....,f_{2n+1 in exp^{-1}(G) such that f_{2n+1} in vect(f_{1},...,f_{2n}) and Z.f_{1}(x)+....+Z.f_{2n+1}(x) is dense subgroup of C^n, where vect(f_{1},....,f_{2n}) is the vector space over R generated by f_{1},....,f_{2n}.