Some results on shadowing and local entropy properties of dynamical systems

2023/09/23 by Noriaki Kawaguchi, Kawaguchi, Noriaki
Mathematics · Physics and Astronomy · #37B40 #37B65 #Advanced Differential Equations and Dynamical Systems #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals #Quantum chaos and dynamical systems

paper · pdf · doi:10.48550/arxiv.2309.13290

openalex publication_date 2023/09/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider some local entropy properties of dynamical systems under the assumption of shadowing. In the first part, we give necessary and sufficient conditions for shadowable points to be certain entropy points. In the second part, we give some necessary and sufficient conditions for (non) h-expansiveness under the assumption of shadowing and chain transitivity; and use the result to present a counter-example for a question raised by Artigue et al. [Proc. Amer. Math. Soc. 150 (2022), 3369-3378].

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