Topological entropy and Hausdorff dimension of irregular sets for non-hyperbolic dynamical systems

2021/03/31 by Pablo G. Barrientos, Yushi Nakano, Artem Raibekas +2
Mathematics · Physics and Astronomy · #Chaos control and synchronization #Combinatorics #Dynamical systems theory #Effective dimension #Entropy (arrow of time) #Fractal #Fractal dimension #Hausdorff dimension #Hausdorff space #Hyperbolic set #Mathematical Dynamics and Fractals #Mathematical analysis #Mathematics #Minkowski–Bouligand dimension #Physics #Pure mathematics #Quantum chaos and dynamical systems #Topological entropy #Topological entropy in physics #Topological quantum number #Topology (electrical circuits) #math.DS

paper · pdf · doi:10.1080/14689367.2022.2031890

published as Dynamical Systems. An International Journal. 2022

openalex created_date 2021/03/29 · openalex publication_date 2022/02/06 · arxiv created 2022/02/14 · arxiv updated 2022/02/16 · openalex updated_date 2026/08/05

Abstract

We systematically investigate examples of non-hyperbolic dynamical systems having irregular sets of full topological entropy and full Hausdorff dimension. The examples include some partially hyperbolic systems and geometric Lorenz flows. We also pose interesting questions for future research.

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