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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…
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…