Searcharxiv⌕ Search

arXiv subjects

Dongmei Zheng

Publications and source records attributed to Dongmei Zheng.

5 recordsLinked to original sources
arXiv2021

Packing topological entropy for amenable group actions

Packing topological entropy is a dynamical analogy of the packing dimension, which can be viewed as a counterpart of Bowen topological entropy. In the present paper, we will give a systematically study to the packing topological entropy for a continuous $G$-action dynamical system $(X,G)$, where $X$ is a compact metric space and $G$ is a countable discrete amenable group. We first prove a variational principle for amenable packing topological entropy: for any Borel subset $Z$ of $X$, the packing topological entropy of $Z$ equals the supremum of upper local entropy over all Borel probability measures for which the subset $Z$ has full measure. And then we obtain an entropy inequality concerning amenable packing entropy. Finally we show that the packing topological entropy of the set of generic points for any invariant Borel probability measure $μ$ coincides with the metric entropy if either $μ$ is ergodic or the system satisfies a kind of specification property.

math.DS↗
arXiv2017

Topological entropy of sets of generic points for actions of amenable groups

Let $G$ be a countable discrete amenable group which acts continuously on a compact metric space $X$ and let $μ$ be an ergodic $G-$invariant Borel probability measure on $X$. For a fixed tempered Følner sequence $\{F_n\}$ in $G$ with $\lim\limits_{n\rightarrow+\infty}\frac{|F_n|}{\log n}=\infty$, we prove the following variational principle: $$h^B(G_μ,\{F_n\})=h_μ(X,G),$$ where $G_μ$ is the set of generic points for $μ$ with respect to $\{F_n\}$ and $h^B(G_μ,\{F_n\})$ is the Bowen topological entropy (along $\{F_n\}$) on $G_μ$. This generalizes the classical result of Bowen in 1973.

math.DS↗
arXiv2016

Bowen entropy for actions of amenable groups

Bowen introduced a definition of topological entropy of subset inspired by Hausdorff dimension in 1973 \cite{B}. In this paper we consider the Bowen's entropy for amenable group action dynamical systems and show that under the tempered condition, the Bowen entropy of the whole compact space for a given Følner sequence equals to the topological entropy. For the proof of this result, we establish a variational principle related to the Bowen entropy and the Brin-Katok's local entropy formula for dynamical systems with amenable group actions.

math.DS↗
arXiv2016

On large deviations for amenable group actions

By proving an amenable version of Katok's entropy formula and handling the quasi tiling techniques, we establish large deviations bounds for countable discrete amenable group actions. This generalizes the classical results of Lai-Sang Young.

math.DS↗