On conjugacy of Smale homeomorphisms

2018/11/19 by В. С. Медведев, Medvedev, V., Евгений Викторович Жужома +1
Mathematics · #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals

paper · pdf · doi:10.48550/arxiv.1811.07764

openalex publication_date 2018/11/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Given closed topological n-manifold Mⁿ, n≥ 2, one introduces the classes of Smale regular SRH(Mⁿ) and Smale semi-regular SsRH(Mⁿ) homeomorphisms of Mⁿ with SRH(Mⁿ)⊂~SsRH(Mⁿ). The class SRH(Mⁿ) contains all Morse-Smale diffeomorphisms, while SsRH(Mⁿ) contains A-diffeomorphisms with trivial and some nontrivial basic sets provided Mⁿ admits a smooth structure. We select invariant sets that determine dynamics of Smale homeomorphisms. This allows us to get necessary and sufficient conditions of conjugacy for SRH(Mⁿ) and SsRH(Mⁿ). We deduce applications for some Morse-Smale diffeomorphisms and A-diffeomorphisms with codimension one expanding attractors.

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