Double variational principle for mean dimension with potential

Masaki Tsukamoto

    Research output: Contribution to journalArticlepeer-review

    16 Citations (Scopus)


    This paper contributes to the mean dimension theory of dynamical systems. We introduce a new concept called mean dimension with potential and develop a variational principle for it. This is a mean dimension analogue of the theory of topological pressure. We consider a minimax problem for the sum of rate distortion dimension and the integral of a potential function. We prove that the minimax value is equal to the mean dimension with potential for a dynamical system having the marker property. The basic idea of the proof is a dynamicalization of geometric measure theory.

    Original languageEnglish
    Article number106935
    JournalAdvances in Mathematics
    Publication statusPublished - Feb 12 2020

    All Science Journal Classification (ASJC) codes

    • General Mathematics


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