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}.
Categories: math.DS