Expansive multiparameter actions and mean dimension

Tom Meyerovitch, Masaki Tsukamoto

Research output: Contribution to journalArticlepeer-review


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 languageAmerican English
Pages (from-to)7275-7299
Number of pages25
JournalTransactions of the American Mathematical Society
Issue number10
StatePublished - 1 Jan 2019


  • Expansive action
  • Mean dimension
  • Topological entropy

All Science Journal Classification (ASJC) codes

  • Applied Mathematics
  • General Mathematics


Dive into the research topics of 'Expansive multiparameter actions and mean dimension'. Together they form a unique fingerprint.

Cite this