论文标题
熵光谱的较弱
Weak rigidity of entropy spectra
论文作者
论文摘要
在本文中，我们考虑了拓扑马尔可夫移位上的熵光谱。我们证明，如果具有Hölder连续电势的Gibbs测量的两个测量的动力学系统是同构的，那么它们的熵光谱是相同的。这个结果提出了一个新的僵化问题。我们将这个问题称为较弱的刚度问题，将其与Barreira和Saraiva提出的强烈刚性问题形成鲜明对比。我们对马尔可夫马尔可夫移动的马尔可夫措施的弱刚性问题提供了完整的答案，其尺寸为2。
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 an aperiodic transition matrix of size 2.
