Entropy Formulae on Feldman-Katok Metric of Random Dynamical Systems
Yunxiang Xie, Ercai Chen, Kexiang Yang
TL;DR
This paper investigates the Feldman-Katok metric in random dynamical systems, establishing entropy formulas and demonstrating its role as the weakest metric ensuring these formulas' validity.
Contribution
It introduces entropy formulas using the Feldman-Katok metric in random dynamical systems and shows its minimality among metrics for these formulas.
Findings
Feldman-Katok metric replaces Bowen metric in entropy formulas.
Established fiber topological, Brin-Katok local, and fiber Katok entropy formulas.
Feldman-Katok metric is the weakest metric for valid entropy formulas.
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.
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Taxonomy
TopicsMeromorphic and Entire Functions · Geometric Analysis and Curvature Flows · Geometry and complex manifolds