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

Part of: Ergodic theory Infinite-dimensional dissipative dynamical systems Random dynamical systems

Published online by Cambridge University Press:  10 July 2025

CHIYI LUO  and
YUN ZHAO
CHIYI LUO
Affiliation:
School of Mathematics and Statistics, Jiangxi Normal University, Nanchang 330022, Jiangxi, P.R. China (e-mail: luochiyi98@gmail.com)
YUN ZHAO*
Affiliation:
Center for Dynamical Systems and Differential Equations, https://ror.org/05t8y2r12School of Mathematical Sciences, Soochow University, Suzhou 215006, Jiangsu, P.R. China
*
e-mail: zhaoyun@suda.edu.cn
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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 [Some ergodic properties of commuting diffeomorphisms. Ergod. Th. & Dynam. Sys. 13(1) (1993), 73–100] about commuting diffeomorphisms in a finite dimensional space to the case of systems on an infinite dimensional Banach space.

Keywords

sub-additivity of entropiescommuting transformationsmultiplicative ergodic theoreminfinite dimensional Banach space

MSC classification

Primary: 37A35: Entropy and other invariants, isomorphism, classification 37H15: Multiplicative ergodic theory, Lyapunov exponents 37L55: Infinite-dimensional random dynamical systems; stochastic equations

Information

Type
Original Article
Information
Ergodic Theory and Dynamical Systems , First View , pp. 1 - 35
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Copyright
© The Author(s), 2025. Published by Cambridge University Press

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