2025/03/31 by Alfonso Artigue, Artigue, Alfonso
Mathematics · Physics and Astronomy · #Dynamical Systems (math.DS) #FOS: Mathematics #Geometric and Algebraic Topology #Mathematical Dynamics and Fractals #Quantum chaos and dynamical systems
paper · pdf · doi:10.48550/arxiv.2504.00168
openalex publication_date 2025/03/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We show that for a compact surface without boundary M the set of cw-expansive homeomorphisms is dense in the set of all the homeomorphisms of M with respect to the C0 topology. After this we show that for a generic homeomorphism f of M it holds that: for all ε>0 there is a cw-expansive homeomorphism g of M which is ε-close to f and is semiconjugate to f; moreover, if π\colon M→ M is this semiconjugacy then π-1(x) is connected, does not separate M and has diameter less than ε for all x∈ M.