Double variational principle for mean dimension

Elon Lindenstrauss, Masaki Tsukamoto

    Research output: Contribution to journalArticlepeer-review

    25 Citations (Scopus)

    Abstract

    We develop a variational principle between mean dimension theory and rate distortion theory. We consider a minimax problem about the rate distortion dimension with respect to two variables (metrics and measures). We prove that the minimax value is equal to the mean dimension for a dynamical system with the marker property. The proof exhibits a new combination of ergodic theory, rate distortion theory and geometric measure theory. Along the way of the proof, we also show that if a dynamical system has the marker property then it has a metric for which the upper metric mean dimension is equal to the mean dimension.

    Original languageEnglish
    Pages (from-to)1048-1109
    Number of pages62
    JournalGeometric and Functional Analysis
    Volume29
    Issue number4
    DOIs
    Publication statusPublished - Aug 1 2019

    All Science Journal Classification (ASJC) codes

    • Analysis
    • Geometry and Topology

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