Weak rigidity of entropy spectra
Weak rigidity of entropy spectra
复制标题
熵谱的弱刚性
DOI：
10.1080/14689367.2021.1876841
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发表时间：
2020
期刊：
影响因子：
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通讯作者：
Katsukuni Nakagawa
中科院分区：
文献类型：
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作者：
Katsukuni Nakagawa
摘要本文研究了拓扑马尔可夫位移上的熵谱。证明了如果两个具有Hölder连续势的Gibbs测度保持测度动力系统同构，则它们的熵谱相同。这个结果引起了一个新的刚性问题。我们称这个问题为弱刚性问题，与Barreira和Saraiva提出的强刚性问题形成对比。本文给出了具有非周期转移矩阵的拓扑马氏位移上马氏测度的弱刚性问题的完整答案。此外，我们证明了一个“非刚性”的结果，持有一定的拓扑马尔可夫移动的非周期转移矩阵。
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 Hölder 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 a aperiodic transition matrix. Moreover, we show that a ‘non-rigidity’ result holds for a certain topological Markov shift with a aperiodic transition matrix.