Topological Entropy, Entropy points and shadowing

2016/11/29 by Seyyed Alireza Ahmadi, Ahmadi, Seyyed Alireza
Mathematics · #Advanced Topology and Set Theory #Dynamical Systems (math.DS) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Mathematical Dynamics and Fractals

paper · pdf · doi:10.48550/arxiv.1611.09493

openalex publication_date 2016/11/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this note we study some properties of topological entropy for non-compact non-metrizable spaces. We prove that if a uniformly continuous self-map f of a uniform space has topological shadowing property then the map f has positive uniform entropy, which extends the similar known result for homeomorphisms on compact metric spaces having shadowing property.

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• Mixing properties of maps with uniform shadowing property in uniform spaces
• Shadowing, sensitivity and entropy points
• Entropy, pseudo-orbit tracing property and positively expansive measures
• Topological entropy for non-uniformly continuous maps
• Entropy of irregular points that are not uniformly hyperbolic