关于玻尔混沌和不变测度概念的几点评述

IF 0.7 3区数学 Q2 MATHEMATICS

Studia Mathematica Pub Date : 2021-09-09 DOI:10.4064/sm230103-13-5

Matan Tal

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引用次数: 1

摘要

玻尔混沌的概念是在[3，4]中引入的。我们回答了[3]中提出的一个问题，即正拓扑熵的非唯一遍历极小系统是否可以是玻尔混沌。我们还证明了所有具有规范性质的系统都是玻尔混沌的，并由此给出了[3]中定理1在可逆系统情况下的独立证明（和加强）。此外，我们还提出了玻尔混沌的一个障碍：一个具有少于遍历不变概率测度连续体的系统不可能是玻尔混沌。

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Some remarks on the notion of Bohr chaos and invariant measures

The notion of Bohr chaos was introduced in [3, 4]. We answer a question raised in [3] of whether a non uniquely ergodic minimal system of positive topological entropy can be Bohr chaotic. We also prove that all systems with the specification property are Bohr chaotic, and by this line of thought give an independent proof (and stengthening) of theorem 1 of [3] for the case of invertible systems. In addition, we present an obstruction for Bohr chaos: a system with fewer than a continuum of ergodic invariant probability measures cannot be Bohr chaotic.

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来源期刊

Studia Mathematica 数学-数学

CiteScore

1.50

自引率

12.50%

发文量

审稿时长

5 months

期刊介绍： The journal publishes original papers in English, French, German and Russian, mainly in functional analysis, abstract methods of mathematical analysis and probability theory.