2019/06/20 by Kengo Matsumoto, Matsumoto, Kengo
Mathematics · #Advanced Operator Algebra Research #Dynamical Systems (math.DS) #FOS: Mathematics #Geometric and Algebraic Topology #Mathematical Dynamics and Fractals #Operator Algebras (math.OA)
paper · pdf · doi:10.48550/arxiv.1906.08441
openalex publication_date 2019/06/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study asymptotic continuous orbit equivalence of Smale spaces. We prove that two irreducible Smale spaces are flip conjugate if and only if there exists a periodic point preserving homeomorphism giving an asymptotic continuous orbit equivalence between them. We introduce a notion of asymptotic topological conjugacy and asymptotic flip conjugacy in Smale spaces and characterize them in terms of the associated Ruelle algebras with dual actioons. We finally characterize the flip conjugacy classes of irreducible two-sided topological Markov shifts in terms of the associated Ruelle algebras with its C^*-subalgebras.