Entropy Formulae on Feldman-Katok Metric of Random Dynamical Systems

2022/08/19 by Yunxiang Xie, Xie, Yunxiang, Ercai Chen +3
Mathematics · #Dynamical Systems (math.DS) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Meromorphic and Entire Functions

paper · pdf · doi:10.48550/arxiv.2208.09146

openalex publication_date 2022/08/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we study the Feldman-Katok metric in random dynamical systems and establish corresponding fiber topological entropy formula, Brin-Katok local entropy formula and fiber Katok entropy formula by replacing Bowen metric with Feldman-Katok metric. It turns out that the Feldman-Katok metric is also the weakest metric that makes the entropy formulae valid on random dynamical systems.

Related

• Variational principles of metric mean dimension for random dynamical systems
• Metric Entropy of Nonautonomous Dynamical Systems
• A new concept of local metric entropy for finite-time nonautonomous dynamical systems
• A variational principle for entropy of a random dynamical system
• Variational principle for neutralized Bowen topological entropy on subsets of non-autonomous dynamical systems