Dynamics of non abelian affine homotheties group of Cⁿ

2011/04/11 by Yahya N'Dao, N'Dao, Yahya, Adlene Ayadi +1
Mathematics · #Advanced Topology and Set Theory #Dynamical Systems (math.DS) #FOS: Mathematics #Geometric and Algebraic Topology #Mathematical Dynamics and Fractals #math.DS

paper · pdf · doi:10.48550/arxiv.1104.2054

arxiv created 2011/04/11 · openalex publication_date 2011/04/11 · arxiv updated 2011/04/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 \E is non empty, every orbit of U is minimal in it.

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