31 citations · 95 across the 35 of their papers we have counts for
35 papers
Maximizing Families and Typical Periodic Optimization for Almost Additive Sequences
XiaoYu Zhang, Ercai Chen, Xiaoyao Zhou
In this paper, we study typical periodic optimization (TPO) for almost additive potentials in two perturbation spaces. Our main setting is the Banach quotient $\mathcal E_{\rm orb}…
Entropy Scales in Topological Dynamical Systems
Yunxiang Xie, Ercai Chen, Xiaoyao Zhou
Motivated by Helfter's notion of scaling, we define Bowen, upper capacity, and local measure-theoretic entropy scales. Under a controlled decay condition, we establish a variationa…
Katok's intermediate entropy conjecture for amenable group actions
Yage Liu, Ercai Chen, Xiaoyao Zhou
In this paper, we investigate a broad class of systems for which Katok's intermediate entropy conjecture holds. In particular, we show that a dynamical system with an amenable grou…
Ergodic measures of intermediate entropies for -action
Yage Liu, Ercai Chen, Xiaoyao Zhou
For dynamical systems satisfying the approximate or -product property and asymptotically entropy expansiveness, we establish a precise descriptio…
Irregular set and metric mean dimension with potential
Tianlong Zhang, Ercai Chen, Xiaoyao Zhou
Let be a dynamical system with the specification property and be a continuous function. In this paper, we consider the multifractal irregular set \begin{align*} I_φ=\le…
Multifractal level sets and metric mean dimension with potential
Tianlong Zhang, Ercai Chen, Xiaoyao Zhou
Let be a dynamical system with the specification property and be continuous functions. In this paper, we establish some conditional variational principles for the upper…
Packing topological pressure for amenable group actions
Ziqing Ding, Ercai Chen, Xiaoyao Zhou
In this paper, we first prove the variational principle for amenable packing topological pressure. Then we obtain an inequality concerning amenable packing pressure for factor maps…
Group Extensions for Random Shifts of Finite Type
Kexiang Yang, Ercai Chen, Zijie Lin +1
Symbolic dynamical theory plays an important role in the research of amenability with a countable group. Motivated by the deep results of Dougall and Sharp, we study the group exte…
Bowen's equations for invariance pressure of control systems
Rui Yang, Ercai Chen, Jiao Yang +1
We aim to establish Bowen's equations for upper capacity invariance pressure and Pesin-Pitskel invariance pressure of discrete-time control systems. We first introduce a new invari…
Non-dense orbit sets carry full metric mean dimension
Jiao Yang, Ercai Chen, Xiaoyao Zhou
Let be a compact metric space, be a continuous transformation with the specification property. we consider non-dense orbit set and show that for…
Upper metric mean dimensions with potential of -stable sets
Rui Yang, Ercai Chen, Xiaoyao Zhou
It is well-known that -stable sets have a deep connection with the topological entropy of dynamical systems. In the present paper, we investigate the relationships of three type…
Variational principle for neutralized Bowen topological entropy
Rui Yang, Ercai Chen, Xiaoyao Zhou
Ovadia and Rodriguez-Hertz defined neutralized Bowen open ball as We introduce the notion of neutrali…
Variational principle for random pressure function
Rui Yang, Ercai Chen, Xiaoyao Zhou
For random dynamical systems, by summarizing the fundamental properties of Kifer's topological pressure we introduce the concept of random pressure functions, and define Ruelle's m…
Weighted Topological Entropy of Random Dynamical Systems
Kexiang Yang, Ercai Chen, Zijie Lin +1
Let be continuous bundle random dynamical systems over an ergodic compact metric system . Assume that ${\bf a}=(a_{1},a_{2})\in\…
On variational principle for upper metric mean dimension with potential
Rui Yang, Ercai Chen, Xiaoyao Zhou
Borrowing the idea of topological pressure determining measure-theoretical entropy in topological dynamical systems, we establish a variational principle for upper metric mean dime…
Some notes on variational principle for metric mean dimension
Rui Yang, Ercai Chen, Xiaoyao Zhou
Firstly, we answer the problem 1 asked by Gutman and piewak in \cite{gs20}, then we establish a double variational principle for mean dimension in terms of R$\bar{…
Metric mean dimension of flows
Rui Yang, Ercai Chen, Xiaoyao Zhou
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 th…
Measure-theoretic metric mean dimension
Rui Yang, Ercai Chen, Xiaoyao Zhou
For infinite measure-theoretic entropy systems, we introduce the notion of measure-theoretic metric mean dimension of invariant measures for different types of measure-theoretic $ε…
Bowen's equations for upper metric mean dimension with potential
Rui Yang, Ercai Chen, Xiaoyao Zhou
Firstly, we introduce a new notion called induced upper metric mean dimension with potential, which naturally generalizes the definition of upper metric mean dimension with potenti…
Mean Li--Yorke chaos and multifractal analysis on subshifts
Zijie Lin, Ercai Chen, Xiaoyao Zhou
In the present paper, we use the generalized multifractal framework introduced by Olsen to study the Bowen entropy and packing entropy of historic sets with typical weights over ap…
Mean dimension theory in symbolic dynamics for finitely generated amenable groups
Yunping Wang, Ercai Chen, Xiaoyao Zhou
In this paper, we mainly elucidate a close relationship between the topological entropy and mean dimension theory for actions of polynomial growth groups. We show that metric mean…
Shadowing and mixing on systems of countable group actions
Zijie Lin, Ercai Chen, Xiaoyao Zhou
Let be a dynamical system, where is compact Hausdorff space, and is a countable discrete group. We investigate shadowing property and mixing between subshifts and…
Entropy and Emergence of Topological Dynamical Systems
Yong Ji, Ercai Chen, Xiaoyao Zhou
A topological dynamical system induces two natural systems, one is on the probability measure spaces and other one is on the hyperspace. We introduce a concept for these tw…
Positive topological entropy and -weakly mixing sets
Wen Huang, Jian Li, Xiangdong Ye +1
The notion of -weakly mixing set is introduced, which shares similar properties of weakly mixing sets. It is shown that if a dynamical system has positive topological entropy, t…