DOUBLE VARIATIONAL PRINCIPLE FOR MEAN DIMENSION WITH POTENTIAL

Masaki Tsukamoto

DOUBLE VARIATIONAL PRINCIPLE FOR MEAN DIMENSION WITH POTENTIAL

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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.

37A05, 37B99, 94A34

Original language	English
Journal	Unknown Journal
Publication status	Published - Jan 17 2019
Externally published	Yes

All Science Journal Classification (ASJC) codes

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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.37A05, 37B99, 94A34",

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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.37A05, 37B99, 94A34

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