Infinite topological entropy, positive mean dimension, and factors of subshifts

2025/04/15 by Jin Lei, Jin, Lei, Yixiao Qiao +1
Computer Science · Materials Science · Mathematics · #Cellular Automata and Applications #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals #Quasicrystal Structures and Properties

paper · pdf · doi:10.48550/arxiv.2504.11040

openalex publication_date 2025/04/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study dynamical systems with the property that all the nontrivial factors have infinite topological entropy (or, positive mean dimension). We establish an ``if and only if'' condition for this property among a typical class of dynamical systems, the subshifts of block type in the Hilbert cube. This in particular leads to a large class of concrete (and new) examples of dynamical systems having this property.

Citations

• Mean topological dimension

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