Sub-additivity of measure-theoretic entropies of commuting transformations on Banach space

2022/03/31 by ChiYi Luo, Yun Zhao, Luo, ChiYi +1
Mathematics · Medicine · #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Biology Tumor Growth #Mathematical Dynamics and Fractals #Mathematical and Theoretical Epidemiology and Ecology Models

paper · pdf · doi:10.48550/arxiv.2203.16961

openalex publication_date 2022/03/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This paper considers two commuting smooth transformations on a Banach space, and proves the sub-additivity of the measure theoretic entropies under mild conditions. Furthermore, some additional conditions are given for the equality of the entropies. This extends Hu's work about commuting diffeomorphisms in a finite dimensional space (Huyi Hu, 1993, Ergod. Th. Dynam. Sys., 13: 73-100) to the case of systems on an infinite dimensional Banach space.

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