Double variational principle for mean dimension with potential

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)

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

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

Fingerprint Dive into the research topics of 'Double variational principle for mean dimension with potential'. Together they form a unique fingerprint.

Cite this