Rigidity of Entropy Spectra for One-Parameter Family of Polynomials
Rigidity of Entropy Spectra for One-Parameter Family of Polynomials
复制标题
一参数多项式族熵谱的刚性
DOI：
10.1007/s00574-021-00274-5
复制
发表时间：
2022
期刊：
影响因子：
--
通讯作者：
Nakagawa Katsukuni
中科院分区：
文献类型：
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作者：
中川勝國;Nakagawa Katsukuni
本文研究了拓扑马氏位移上马氏测度的熵谱。对于移位上的马尔可夫测度，利用矩阵理论对它的熵谱的描述，我们自然地得到了一个单参数多项式族。我们考虑一组所有马尔可夫措施的转变，其熵谱的所有信息的家庭的多项式，不像Barreira和Saraiva谁认为一组的熵谱的所有信息的等价类的关系引起的行动的自同构群的转变。我们给出了一个充分条件的移动，我们的集合包含一个满测度开集的空间上的所有移动的马尔可夫措施。这个刚性结果与Barreira和Saraiva的非刚性结果相反，Barreira和Saraiva的非刚性结果是，对于某个拓扑马尔可夫移位，其集合的补包含移位上的所有马尔可夫测度的空间的全测度开集。巴雷拉和萨莱瓦的移位满足我们的条件，因此，移位在我们的意义上是刚性的。
In this paper, we consider entropy spectra of Markov measures on topological Markov shifts. For a Markov measure on a shift, using the description of its entropy spectrum via matrix theory, we naturally obtain a one-parameter family of polynomials. We consider the set of all Markov measures on the shift whose entropy spectra have all information about the families of polynomials, unlike Barreira and Saraiva who considered the set of those whose entropy spectra have all information about the equivalence classes of the relation induced by the action of the automorphism group of the shift. We give a sufficient condition on a shift for our set to contain a full-measure open set of the space of all Markov measures on the shift. This rigidity result is in contrast to the non-rigidity result of Barreira and Saraiva that, for a certain topological Markov shift, the complement of their set contains a full-measure open set of the space of all Markov measures on the shift. The shift of Barreira and Saraiva satisfies our condition, and hence, the shift turns out to be rigid in our sense.
分段线性马尔可夫映射的多重分形刚性
影响因子：
1.1
作者：
Katsukuni Nakagawa
通讯作者：
Katsukuni Nakagawa
DOI：
10.1080/14689367.2021.1876841
发表时间：
2020
期刊：
Dynamical Systems
影响因子：
--
作者：
Katsukuni Nakagawa
通讯作者：
Katsukuni Nakagawa