Lowering topological entropy over subsets

2008/11/26 by Wen Huang, Xiangdong Ye, Huang, Wen +3 · 2 citations
Mathematics · #Mathematical Dynamics and Fractals #Advanced Topology and Set Theory

paper · pdf · doi:10.48550/arxiv.0811.4230

Abstract

Let (X, T) be a topological dynamical system (TDS), and h (T, K) the topological entropy of a subset K of X. (X, T) is \it lowerable if for each 0≤ h≤ h (T, X) there is a non-empty compact subset with entropy h; is \it hereditarily lowerable if each non-empty compact subset is lowerable; is \it hereditarily uniformly lowerable if for each non-empty compact subset K and each 0≤ h≤ h (T, K) there is a non-empty compact subset K_h⊆ K with h (T, K_h)= h and K_h has at most one limit point. It is shown that each TDS with finite entropy is lowerable, and that a TDS (X, T) is hereditarily uniformly lowerable if and only if it is asymptotically h-expansive.

Citations

• Topological entropy for noncompact sets
• Mean topological dimension

Cited by

• Lowering topological entropy over subsets for amenable group actions
• Entropy Flexibility of Dynamical Systems

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