# Double variational principle for mean dimension with potential

Masaki Tsukamoto

8 被引用数 (Scopus)

## 抄録

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.

本文言語 英語 106935 Advances in Mathematics 361 https://doi.org/10.1016/j.aim.2019.106935 出版済み - 2月 12 2020

• 数学 (全般)

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