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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…
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 typ…
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 $Î…
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_Ï=\…
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 uppe…
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…