# 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 language English 106935 Advances in Mathematics 361 https://doi.org/10.1016/j.aim.2019.106935 Published - 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

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

Research output: Contribution to journalArticle

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