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arXiv · 2203.16961

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

ChiYi Luo·Yun Zhao
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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., \textbf{13}: 73-100) to the case of systems on an infinite dimensional Banach space.

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ChiYi Luo, Yun Zhao. 2022-03-31. Sub-additivity of measure-theoretic entropies of commuting transformations on Banach space. https://doi.org/10.1017/etds.2025.10197

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