Weak rigidity of entropy spectra

Katsukuni Nakagawa

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arXiv · 2009.06256

Weak rigidity of entropy spectra

Katsukuni Nakagawa

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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.

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Katsukuni Nakagawa. 2020-09-14. Weak rigidity of entropy spectra. https://arxiv.org/abs/2009.06256

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