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arXiv · 1901.05628

Double variational principle for mean dimension with potential

Masaki Tsukamoto
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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.

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Masaki Tsukamoto. 2019-01-17. Double variational principle for mean dimension with potential. https://arxiv.org/abs/1901.05628

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