Double variational principle for mean dimension with potential

Research output: Contribution to journalArticle

Abstract

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
Volume361
DOIs
Publication statusPublished - Feb 12 2020

Fingerprint

Variational Principle
Dynamical system
Geometric Measure Theory
Topological Pressure
Dimension Theory
Minimax Problems
Rate-distortion
Potential Function
Minimax
Analogue

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

Cite this

Double variational principle for mean dimension with potential. / Tsukamoto, Masaki.

In: Advances in Mathematics, Vol. 361, 106935, 12.02.2020.

Research output: Contribution to journalArticle

@article{3ae0fe44af5c4ebb909d7f474b6847d6,
title = "Double variational principle for mean dimension with potential",
abstract = "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.",
author = "Masaki Tsukamoto",
year = "2020",
month = "2",
day = "12",
doi = "10.1016/j.aim.2019.106935",
language = "English",
volume = "361",
journal = "Advances in Mathematics",
issn = "0001-8708",
publisher = "Academic Press Inc.",

}

TY - JOUR

T1 - Double variational principle for mean dimension with potential

AU - Tsukamoto, Masaki

PY - 2020/2/12

Y1 - 2020/2/12

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=85076246086&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85076246086&partnerID=8YFLogxK

U2 - 10.1016/j.aim.2019.106935

DO - 10.1016/j.aim.2019.106935

M3 - Article

AN - SCOPUS:85076246086

VL - 361

JO - Advances in Mathematics

JF - Advances in Mathematics

SN - 0001-8708

M1 - 106935

ER -