Correlation entropy of free semigroup actions

2024/06/26 by Xiaojiang Ye, Yanjie Tang, Ye, Xiaojiang +3
Mathematics · Physics and Astronomy · #Chaos control and synchronization #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals

paper · pdf · doi:10.48550/arxiv.2406.18147

openalex publication_date 2024/06/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This paper introduces the concepts of correlation entropy and local correlation entropy for free semigroup actions on compact metric space, and explores their fundamental properties. Thereafter, we generalize some classical results on correlation entropy and local correlation entropy to apply to free semigroup actions. Finally, we establish the relationship between topological entropy, measure-theoretic entropy, correlation entropy, and local correlation entropy for free semigroup actions under various conditions.

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