Dynamics of non abelian affine homotheties group of Cn
Abstract
In this paper we study the action of non abelian subgroup G generated by affine homotheties on Cn. We prove that there exist a subgroup H of C\0, a G-invariant affine subspace E of Cn and b in E such that the closure of any orbit G(z) is equal to H(z-a)+E, z in Cn. In particular, every orbit in E is dense in it. Moreover, if the complementary U=Cn is non empty, every orbit of U is minimal in it.
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