相关论文: A variational principle for the metric mean dimens…

We establish three variational principles for the upper metric mean dimension with potential of level sets of continuous maps in terms of the entropy of partitions and Katok's entropy of the underlying system. Our results hold for dynamical…

Borrowing the idea of topological pressure determining measure-theoretical entropy in topological dynamical systems, we establish a variational principle for upper metric mean dimension with potential in terms of upper measure-theoretical…

Let $(X,f)$ be a dynamical system with the specification property and $\varphi$ be continuous functions. In this paper, we establish some conditional variational principles for the upper and lower Bowen/packing metric mean dimension with…

In this article, we introduce a notion of relative mean metric dimension with potential for a factor map $\pi: (X,d, T)\to (Y, S)$ between two topological dynamical systems. To link it with ergodic theory, we establish four variational…

We study variational principles for metric mean dimension. First we prove that in the variational principle of Lindenstrauss and Tsukamoto it suffices to take supremum over ergodic measures. Second we derive a variational principle for…

In this note, we show several variational principles for metric mean dimension. First we prove a variational principles in terms of Shapira's entropy related to finite open covers. Second we establish a variational principle in terms of…

Metric mean dimension is a dynamical counterpart of the box dimension in fractal geometry to characterize the topological complexity of infinite entropy systems. The classical variational principle states that topological entropy equals the…

It is well-known that the relativized variational principle established by Bogenschutz and Kifer connects the fiber topological entropy and fiber measure-theoretic entropy. In context of random dynamical systems, metric mean dimension was…

Firstly, we answer the problem 1 asked by Gutman and $\rm \acute{\ S}$piewak in \cite{gs20}, then we establish a double variational principle for mean dimension in terms of R$\bar{e}$nyi information dimension and show the order of $\sup$…

Let $(X,d)$ be a compact metric space, $f:X \mapsto X$ be a continuous map with the specification property, and $\varphi: X \mapsto \IR$ be a continuous function. We prove a variational principle for topological pressure (in the sense of…

It is well-known that $\epsilon$-stable sets have a deep connection with the topological entropy of dynamical systems. In the present paper, we investigate the relationships of three types of upper metric mean dimensions with potential…

This paper investigates the relationship between quantization of measures and metric mean dimension of topological dynamical systems. We introduce the concept of mean quantization dimension for invariant probability measures and establish a…

This paper contributes to the mean dimension theory of dynamical systems. We introduce a new concept called mean dimension with potential and develop a variational principle for it. This is a mean dimension analogue of the theory of…

We develop a variational principle for mean dimension with potential of $\mathbb{R}^d$-actions. We prove that mean dimension with potential is bounded from above by the supremum of the sum of rate distortion dimension and a potential term.…

The goal of this paper is to define and investigate those topological pressures, which is an extension of topological entropy presented by Feng and Huang [13], of continuous transformations. This study reveals the similarity between many…

Around the mean dimensions and rate-distortion functions, using some tools from local entropy theory this paper establishes the following main results: $(1)$ We prove that for non-ergodic measures associated with almost sure processes, the…

We prove a variational principle for the metric mean dimension analog to the one in [LT]. Instead of using the rate distortion function we use the function $h_\mu(\epsilon,T,\delta)$ that is closely related to the entropy $h_\mu(T)$ of…

We introduce the notion of Feldman-Katok metric mean dimensions in this note. We show metric mean dimensions defined by different metrics coincide under weak tame growth of covering numbers, and establish variational principles for…

For dynamical systems with infinite topological entropy, the classical entropy fails to quantify their complexity effectively, while the metric mean dimension provides a natural extension in this context. In this paper, we study the…

The present paper aims to investigate the metric mean dimension theory of continuous flows. We introduce the notion of metric mean dimension for continuous flows to characterize the complexity of flows with infinite topological entropy. For…