可数群的正熵作用影响伯努利位移

IF 3.5 1区数学 Q1 MATHEMATICS

Journal of the American Mathematical Society Pub Date : 2018-04-14 DOI:10.1090/JAMS/931

Brandon Seward

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引用次数: 16

摘要

我们证明了如果可数无限群的自由遍历作用具有正的Rokhlin熵(或者更一般地说，正的sofic熵)，那么它就会因子化到所有较小或相等熵的伯努利位移上。这将经典熵理论中著名的西奈因子定理推广到所有可数无限群。

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Positive entropy actions of countable groups factor onto Bernoulli shifts

We prove that if a free ergodic action of a countably infinite group has positive Rokhlin entropy (or, less generally, positive sofic entropy), then it factors onto all Bernoulli shifts of lesser or equal entropy. This extends to all countably infinite groups the well-known Sinai factor theorem from classical entropy theory.

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来源期刊

Journal of the American Mathematical Society 数学-数学

CiteScore

7.60

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： All articles submitted to this journal are peer-reviewed. The AMS has a single blind peer-review process in which the reviewers know who the authors of the manuscript are, but the authors do not have access to the information on who the peer reviewers are. This journal is devoted to research articles of the highest quality in all areas of pure and applied mathematics.