Metric mean dimension of irregular sets for maps with shadowing

2022/11/07 by Magdalena Foryś-Krawiec, Piotr Oprocha, Foryś-Krawiec, Magdalena +1
Mathematics · #Analytic and geometric function theory #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals

paper · pdf · doi:10.48550/arxiv.2211.03503

openalex publication_date 2022/11/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study the metric mean dimension of Φ-irregular set I_Φ(f) in dynamical systems with the shadowing property. In particular we prove that for dynamical systems with shadowing containing a chain recurrent class Y, the values of topological entropy together with the values of lower and upper metric mean dimension of the set I_Φ(f)∩ B(Y,ε)∩ CR(f) are bounded from below by the respective values for class Y.

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