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arXiv · 2102.10281

Packing entropy for fixed-point free flows

Ruiming Liang·Haoyi Lei
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Abstract

Let $(X,ϕ)$ be a compact flow without fixed points. We define the packing topological entropy $h_{\mathrm{top}}^P(ϕ,K)$ 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 $X$, $$h_{\mathrm{top}}^P(ϕ,K)=\sup\{\overline{h}_μ(ϕ):μ(K)=1,μ\text{ is a Borel probability measure on} X\},$$ where $\overline{h}_μ(ϕ)$ denotes the upper local entropy for a Borel probability measure $μ$ on $X$.

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Ruiming Liang, Haoyi Lei. 2021-02-20. Packing entropy for fixed-point free flows. https://arxiv.org/abs/2102.10281

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