Double variational principle for mean dimension

Elon Lindenstrauss, Masaki Tsukamoto

研究成果: Contribution to journalArticle査読

6 被引用数 (Scopus)

抄録

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.

本文言語英語
ページ(範囲)1048-1109
ページ数62
ジャーナルGeometric and Functional Analysis
29
4
DOI
出版ステータス出版済み - 8 1 2019
外部発表はい

All Science Journal Classification (ASJC) codes

  • 分析
  • 幾何学とトポロジー

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