Dynamics of non abelian affine homotheties group of C^n

Yahya N'Dao; Adlene Ayadi

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arXiv · 1104.2054

Dynamics of non abelian affine homotheties group of C^n

Yahya N'Dao·Adlene Ayadi

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Abstract

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

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Yahya N'Dao, Adlene Ayadi. 2011-04-11. Dynamics of non abelian affine homotheties group of C^n. https://arxiv.org/abs/1104.2054

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