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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…
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…
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…
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…
Dimensions and entropies for an expansive homeomorphism
Ercai Chen, Tassilo Küpper, Yunxiang Xie
For an expansive homeomorphism, we investigate the relationship among dimension, entropy, and Lyapunov exponents. Motivated by Young's formula for surface diffeomorphisms, which li…
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…