Expansive multiparameter actions and mean dimension

Tom Meyerovitch, Masaki Tsukamoto

    Research output: Contribution to journalArticlepeer-review

    10 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 - 2019

    All Science Journal Classification (ASJC) codes

    • General Mathematics
    • Applied Mathematics

    Fingerprint

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

    Cite this