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 |
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Article number | 106935 |
Journal | Advances in Mathematics |
Volume | 361 |
DOIs | |
Publication status | Published - Feb 12 2020 |
All Science Journal Classification (ASJC) codes
- Mathematics(all)