2021/11/08 by В. С. Медведев, Medvedev, Vladislav, Евгений Викторович Жужома +1
Mathematics · #37D15 #Dynamical Systems (math.DS) #FOS: Mathematics #Geometric and Algebraic Topology #Geometry and complex manifolds #Mathematical Dynamics and Fractals
paper · pdf · doi:10.48550/arxiv.2111.04246
openalex publication_date 2021/11/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We introduce Smale A-homeomorphisms that includes regular, semi-chaotic, chaotic, and super chaotic homeomorphisms of topo\-lo\-gi\-cal n-manifold Mn, n≥ 2. Smale A-homeo\-mor\-p\-hisms contain A-diffeomorphisms (in particular, structurally stable diffeomorphisms) provided Mn admits a smooth structure. Regular A-homeomorphisms contain all Morse-Smale diffeomorphisms, while semi-chaotic and chaotic A-homeomorphisms contain A-diffeo\-mor\-p\-hisms with trivial and nontrivial basic sets. Super chaotic A-homeo\-mor\-p\-hisms contain A-diffeomorphisms whose basic sets are nontrivial. We describe invariant sets that determine completely dynamics of regular, semi-chaotic, and chaotic Smale A-homeo\-mor\-p\-hisms. This allows us to get necessary and sufficient conditions of conjugacy for these Smale A-homeomorp\-hisms. We apply this necessary and sufficient conditions for structu\-ral\-ly stable surface diffeomorphisms with arbitrary number of one-dimensional expanding attractors. We also use this conditions to get the complete classification of Morse-Smale diffeomorphisms on projective-like n-manifolds for n=2,8,16.