Lowering topological entropy over subsets revisited

2012/06/04 by Wen Huang, Xiangdong Ye, Huang, Wen +3 · 1 citation
Biochemistry, Genetics and Molecular Biology · Mathematics · #Advanced Topology and Set Theory #Caveolin-1 and cellular processes #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals

paper · pdf · doi:10.48550/arxiv.1206.0518

openalex publication_date 2012/06/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let (X, T) be a topological dynamical system. Denote by h (T, K) and h^B (T, K) the covering entropy and dimensional entropy of K⊆ X, respectively. (X, T) is called D-\it lowerable (resp. \it lowerable) if for each 0≤ h≤ h (T, X) there is a subset (resp. closed subset) K_h with h^B (T, K_h)= h (resp. h (T, K_h)= h); is called D-\it hereditarily lowerable (resp. \it hereditarily lowerable) if each Souslin subset (resp. closed subset) is D-lowerable (resp. lowerable). In this paper it is proved that each topological dynamical system is not only lowerable but also D-lowerable, and each asymptotically h-expansive system is D-hereditarily lowerable. A minimal system which is lowerable and not hereditarily lowerable is demonstrated.

Citations

• Topological entropy for noncompact sets
• Mean topological dimension

Cited by

• Lowering topological entropy over subsets for amenable group actions

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