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A variational principle of scaled entropy for amenable group actions

Part of: Topological dynamics Dynamical systems with hyperbolic behavior

Published online by Cambridge University Press:  09 January 2025

Yu Liu  and
Zhiming Li
Yu Liu
Affiliation:
School of Mathematics, Northwest University, Xi’an, P.R. China e-mail: liuyu_yzr@126.com
Zhiming Li*
Affiliation:
School of Mathematics, Northwest University, Xi’an, P.R. China e-mail: liuyu_yzr@126.com
*
e-mail: china-lizhiming@163.com
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Abstract

We study scaled topological entropy, scaled measure entropy, and scaled local entropy in the context of amenable group actions. In particular, a variational principle is established.

Keywords

Scaled topological entropyscaled measure entropyscaled local entropyvariational principle

MSC classification

Primary: 37D35: Thermodynamic formalism, variational principles, equilibrium states 37B05: Transformations and group actions with special properties (minimality, distality, proximality, etc.)
Secondary: 37B40: Topological entropy
Type
Article
Information
Canadian Journal of Mathematics , First View , pp. 1 - 28
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Copyright
© The Author(s), 2025. Published by Cambridge University Press on behalf of Canadian Mathematical Society

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