Packing entropy for fixed-point free flows

Abstract

Let $(X,\varphi )$ be a compact flow without fixed points. We define the packing topological entropy $h_{\mathrm{top}}^P(\varphi ,K)$ on subsets of $X$ through considering all the possible reparametrizations of time. For fixed-point free flows, we prove the following result: for any non-empty compact subset $K$ of $X$, $$h_{\mathrm{top}}^P(\varphi ,K)=\sup \{{\overline{h}}_{\mu }(\varphi ):\mu (K)=1,\mu \text{ is a Borel probability measure on}X\},$$ where ${\overline{h}}_{\mu }(\varphi )$ denotes the upper local entropy for a Borel probability measure $\mu$ on $X$.

References in corpus (1)

• Packing topological entropy for amenable group actions