2024/05/27 by Mayara Braz Antunes, Bernardo Carvalho, Antunes, Mayara +5 · 1 citation
Computer Science · Mathematics · #Computability, Logic, AI Algorithms #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals #Topological and Geometric Data Analysis
paper · pdf · doi:10.48550/arxiv.2405.17574
openalex publication_date 2024/05/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We prove that local stable/unstable sets of homeomorphisms of an infinite compact metric space satisfying the gluing-orbit property always contain compact and perfect subsets of the space. As a consequence, we prove that if a positively countably expansive homeomorphism satisfies the gluing-orbit property, then the space is a single periodic orbit. We also prove that there are homeomorphisms with gluing-orbit such that its induced homeomorphism on the hyperspace of compact subsets does not have gluing-orbit, contrasting with the case of the shadowing and specification properties, proving that if the induced map has gluing-orbit, then the base map has gluing-orbit and is topologically mixing.