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Conditional mean dimension

Part of: Spaces with richer structures

Published online by Cambridge University Press:  06 September 2021

BINGBING LIANG Open the ORCID record for BINGBING LIANG [Opens in a new window]
BINGBING LIANG*
Affiliation:
Department of Mathematical Science, Soochow University, Suzhou 215006, China The Institute of Mathematics of the Polish Academy of Sciences, ul. Śniadeckich 8, Warsaw 00-656, Poland (e-mail: bliang@impan.pl)
*
e-mail: bbliang@suda.edu.cn
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Abstract

We introduce some notions of conditional mean dimension for a factor map between two topological dynamical systems and discuss their properties. With the help of these notions, we obtain an inequality to estimate the mean dimension of an extension system. The conditional mean dimension for G-extensions is computed. We also exhibit some applications in dynamical embedding problems.

Keywords

amenable groupconditional mean dimensionG-extensiondynamical embedding

MSC classification

Secondary: 54E45: Compact (locally compact) metric spaces
Type
Original Article
Information
Ergodic Theory and Dynamical Systems , Volume 42 , Issue 10 , October 2022 , pp. 3152 - 3166
Copyright
© The Author(s), 2021. Published by Cambridge University Press

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