Embedding minimal dynamical systems into Hilbert cubes

Yonatan Gutman, Masaki Tsukamoto

    Research output: Contribution to journalArticlepeer-review

    20 Citations (Scopus)


    We study the problem of embedding minimal dynamical systems into the shift action on the Hilbert cube ([0,1]N)Z. This problem is intimately related to the theory of mean dimension, which counts the average number of parameters for describing a dynamical system. Lindenstrauss proved that minimal systems of mean dimension less than cN for c= 1 / 36 can be embedded in ([0,1]N)Z, and asked what is the optimal value for c. We solve this problem by showing embedding is possible when c= 1 / 2. The value c= 1 / 2 is optimal. The proof exhibits a new interaction between harmonic analysis and dynamical coding techniques.

    Original languageEnglish
    Pages (from-to)113-166
    Number of pages54
    JournalInventiones Mathematicae
    Issue number1
    Publication statusPublished - Jul 1 2020

    All Science Journal Classification (ASJC) codes

    • Mathematics(all)


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