Double variational principle for mean dimension with potential
Dynamical Systems
2019-01-28 v1 Information Theory
math.IT
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.
Keywords
Cite
@article{arxiv.1901.05628,
title = {Double variational principle for mean dimension with potential},
author = {Masaki Tsukamoto},
journal= {arXiv preprint arXiv:1901.05628},
year = {2019}
}
Comments
46 pages, 3 figures. arXiv admin note: text overlap with arXiv:1901.05623