Weak rigidity of entropy spectra
Dynamical Systems
2020-09-28 v2
Abstract
In this paper, we consider entropy spectra on topological Markov shifts. We prove that if two measure-preserving dynamical systems of Gibbs measures with H\"older continuous potentials are isomorphic, then their entropy spectra are the same. This result raises a new rigidity problem. We call this problem the weak rigidity problem, contrasting it with the strong rigidity problem proposed by Barreira and Saraiva. We give a complete answer to the weak rigidity problem for Markov measures on a topological Markov shift with an aperiodic transition matrix of size 2.
Cite
@article{arxiv.2009.06256,
title = {Weak rigidity of entropy spectra},
author = {Katsukuni Nakagawa},
journal= {arXiv preprint arXiv:2009.06256},
year = {2020}
}