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 |
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論文番号 | 106935 |
ジャーナル | Advances in Mathematics |
巻 | 361 |
DOI | |
出版ステータス | 出版済み - 2月 12 2020 |
!!!All Science Journal Classification (ASJC) codes
- 数学 (全般)