Amenable upper mean dimensions
type: Item
instance of: scholarly article
title: Amenable upper mean dimensions
zbMATH Open document ID: 1480.37038
author: Zhiming Li
published in: Analysis and Mathematical Physics
publication date: 2021-06-30T00:00:00Z
review text: This paper is devoted to the notion of upper measure-theoretic mean dimension and to the variational principle of upper metric mean dimensions. It is known that the entropy is the most important invariant to measure the complexity of dynamical systems. Furthermore, it plays an essential role in information theory, dimension theory and fractal geometry. A part of this paper is devoted to the concept of mean dimension, its applications, and variational principles. The main goal of this work is a formulation of upper metric mean dimension and upper measure-theoretic mean dimension for amenable group actions. A relation between upper metric mean dimensions and pseudo-orbits is also discussed.
reviewed by: Symon Serbenyuk
Mathematics Subject Classification ID: 37C45
Mathematics Subject Classification ID: 37A25
Mathematics Subject Classification ID: 37D35
Mathematics Subject Classification ID: 37C85
Mathematics Subject Classification ID: 37B05
Mathematics Subject Classification ID: 28D20
Mathematics Subject Classification ID: 37B65
zbMATH DE Number: 7365501
zbMATH Keywords: amenable group action
zbMATH Keywords: mean dimension
zbMATH Keywords: variational principle
MaRDI profile type: Publication
full work available at URL: s13324-021-00538-9
OpenAlex ID: W3161539175
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DOI: 10.1007/S13324-021-00538-9
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description: scientific article; zbMATH DE number 7365501