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Mean topological dimension of a random dynamical system for amenable groups

Part of: Random dynamical systems Ergodic theory

Published online by Cambridge University Press:  07 July 2025

Yu Liu  and
Xiaojun Huang
Yu Liu
Affiliation:
College of Mathematics and Statistics, Chongqing University, Chongqing, China
Xiaojun Huang*
Affiliation:
College of Mathematics and Statistics, Chongqing University, Chongqing, China
*
Corresponding author: Xiaojun Huang, email: mathhxj@163.com
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Abstract

We introduce the mean topological dimension of random bundle transformations associated with an infinite countable discrete amenable group action and show that continuous bundle random dynamical systems for amenable groups with finite fibre topological entropy have zero mean topological dimensions.

Keywords

bundle random dynamical systemmean topological dimensionmetric mean dimensionamenable group

MSC classification

Primary: 37A35: Entropy and other invariants, isomorphism, classification
Secondary: 37H05: Foundations, general theory of cocycles, algebraic ergodic theory

Information

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , First View , pp. 1 - 32
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Copyright
© The Author(s), 2025. Published by Cambridge University Press on behalf of The Edinburgh Mathematical Society.

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