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Zhongxuan Yang

Publications and source records attributed to Zhongxuan Yang.

4 recordsLinked to original sources
arXiv2025

Variational principles for BS dimension under amenable group actions

In this manuscript, we focus on the investigation of the BS dimension and BS packing dimension under amenable group actions. Firstly, we obtain a Bowen's equation which illustrate the relation of BS packing dimension to the packing topological pressure under amenable group actions. Moreover, we establish the variational principle and inverse variational principle for BS dimension and BS packing dimension under amenable group actions. Finally, we also get an analogue of Billingsley's type theorem for BS packing dimension under amenable group actions.

math.DS↗
arXiv2024

A note on weak mean equicontinuity and strong mean sensitivity

In this paper, we study the weak mean metric and give some properties by replacing the Besicovitch pseudometric with weak mean metric in the definition of mean equicontinuity and mean sensitivity. We study an opposite side of weak mean equicontinuity, strong mean sensitivity and we obtain a version of Auslander-Yorke dichotomies: minimal topological dynamical systems are either weak mean equicontinuous or strong mean sensitive, and transitive topological dynamical systemss are either almost weak mean equicontinuous or strong mean sensitive. Furthermore, motivated by the localized idea of sensitivity, we introduce some notions of new version sensitive tuples and study the properties of these sensitive tuples, we show that a transitive dynamical system is strong mean sensitive if and only if it admits a strong mean sensitive tuple. Finally, We introduce the notions of weakly mean equicontinuity of a topological dynamical system respect to a given continuous function $f$, and we show that a topological dynamical system is weakly mean equicontinuity then it is weakly mean equicontinuity with respect to every continuous function.

math.DS↗
arXiv2024

A note on weak Banach mean equicoontinuity

Consider a topological dynamical system $(X, T)$ endowed with the metric $d$. We introduce a novel function as $\overline{BF}(x, y) = \limsup_{n-m \rightarrow +\infty} \inf_{σ\in S_{n,m}} \frac{1}{n-m} \sum_{k=m}^{n-1} d\left(T^{k} x, T^{σ(k)} y\right)$, where the permutation group $S_{n,m}$ is utilized. It is demonstrated that $BF(x, y)$ exists when $x, y \in X$ are uniformly generic points. Leveraging this function, we introduce the concept of weak Banach mean equicontinuity and establish that the dynamical system $(X, T)$ exhibits weak Banach mean equicontinuity if and only if the uniform time averages $f_B^{*}(x) = \lim_{n-m \rightarrow +\infty} \frac{1}{n-m} \sum_{k=m}^{n-1} f\left(T^{k} x\right)$ are continuous for all $f \in C(X)$. Finally, we demonstrate that in the case of a transitive system, the equivalence between weak Banach mean equicontinuity and weak mean equicontinuity is established.

math.DS↗