Sufficient conditions for non-zero entropy of closed relations

IF 0.8 3区数学 Q2 MATHEMATICS

Ergodic Theory and Dynamical Systems Pub Date : 2024-02-15 DOI:10.1017/etds.2024.11

IZTOK BANIČ, RENE GRIL ROGINA, JUDY KENNEDY, VAN NALL

引用次数: 0

Abstract

We introduce the notions of returns and well-aligned sets for closed relations on compact metric spaces and then use them to obtain non-trivial sufficient conditions for such a relation to have non-zero entropy. In addition, we give a characterization of finite relations with non-zero entropy in terms of Li–Yorke and DC2 chaos.

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封闭关系熵不为零的充分条件

我们为紧凑度量空间上的闭合关系引入了返回集和对齐集的概念，然后利用它们得到了这种关系具有非零熵的非难充分条件。此外，我们还从李-约克混沌和 DC2 混沌的角度给出了具有非零熵的有限关系的特征。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Ergodic Theory and Dynamical Systems 数学-数学

CiteScore

1.70

自引率

11.10%

发文量

113

审稿时长

6-12 weeks

期刊介绍： Ergodic Theory and Dynamical Systems focuses on a rich variety of research areas which, although diverse, employ as common themes global dynamical methods. The journal provides a focus for this important and flourishing area of mathematics and brings together many major contributions in the field. The journal acts as a forum for central problems of dynamical systems and of interactions of dynamical systems with areas such as differential geometry, number theory, operator algebras, celestial and statistical mechanics, and biology.