Expansive multiparameter actions and mean dimension

Tom Meyerovitch, Masaki Tsukamoto

Research output: Contribution to journalArticle

2 Citations (Scopus)

Abstract

Mañé proved in 1979 that if a compact metric space admits an expansive homeomorphism, then it is finite dimensional. We generalize this theorem to multiparameter actions. The generalization involves mean dimension theory, which counts the “averaged dimension” of a dynamical system. We prove that if T: ℤk ×X → X is expansive and if R: ℤk −1 ×X → X commutes with T, then R has finite mean dimension. When k = 1, this statement reduces to Mañé’s theorem. We also study several related issues, especially the connection with entropy theory.

Original languageEnglish
Pages (from-to)7275-7299
Number of pages25
JournalTransactions of the American Mathematical Society
Volume371
Issue number10
DOIs
Publication statusPublished - Jan 1 2019
Externally publishedYes

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Dynamical systems
Entropy
Dimension Theory
Compact Metric Space
Homeomorphism
Commute
Theorem
Count
Dynamical system
Generalise
Generalization

All Science Journal Classification (ASJC) codes

  • Mathematics(all)
  • Applied Mathematics

Cite this

Expansive multiparameter actions and mean dimension. / Meyerovitch, Tom; Tsukamoto, Masaki.

In: Transactions of the American Mathematical Society, Vol. 371, No. 10, 01.01.2019, p. 7275-7299.

Research output: Contribution to journalArticle

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