Minimal amenable subshift with full mean dimension

2024/06/12 by Zhengyu Yin, Yin, Zhengyu, Zubiao Xiao +1
Computer Science · Engineering · #Advanced Materials and Mechanics #Cellular Automata and Applications #Dynamical Systems (math.DS) #FOS: Mathematics #Modular Robots and Swarm Intelligence

paper · pdf · doi:10.48550/arxiv.2406.08280

openalex publication_date 2024/06/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let G be an infinite countable amenable group and P a polyhedron with topological dimension dim(P)<∞. We construct a minimal subshift (X,G) such that its mean topological dimension is equal to dim(P). This result answers the question of D. Dou in \citeDD, moreover, it is also an extension of the work of L. Jin and Y. Qiao \citeJQ for ℤ-action.

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