完备度量空间中的混沌判定

吴小英, 陈员龙, 王芬

数学学报 ›› 2021, Vol. 64 ›› Issue (2) : 225-230.

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数学学报 ›› 2021, Vol. 64 ›› Issue (2) : 225-230. DOI: 10.12386/A2021sxxb0019
论文

完备度量空间中的混沌判定

    吴小英, 陈员龙, 王芬
作者信息 +

Chaotic Criteria in Complete Metric Spaces

    Xiao Ying WU, Yuan Long, CHEN Fen WANG
Author information +
文章历史 +

摘要

本文研究完备度量空间上的离散动力系统的混沌标准，证明了如果完备度量空间X上的连续映射f具有正则非退化返回排斥子或连接不动点的正则非退化异宿环，则存在f的不变闭子集Λ，使得f限制在此不变闭子集上的子系统与两个符号的符号动力系统拓扑共轭，从而获得具有这类结构的连续映射f具有Devaney混沌、分布混沌、正拓扑熵及ω-混沌，此结果改进了已有的相关结果.

Abstract

In this paper, the chaotic criteria of discrete dynamical systems is studied in complete metric spaces. It is showed that if f is continuous map from a complete metric space X into itself and has regular nondegenrate snap-back repellers or heteroclinic repellers, then there exists an invariant subset Λ of f such that (Λ, f) is topologically conjugate to the one-side symbolic system (Σ+2, σ). Therefore, f is Devaney's chaos, distributional chaos, ω-chaos and has positive entropy. These results improve the related results.

关键词

离散动力系统 / Devaney混沌 / 分布混沌 / 返回排斥子 / 拓扑共轭

Key words

discrete dynamical system / Devaney's chaos / distributional chaos / snapback repellers / topological conjugation

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吴小英, 陈员龙, 王芬. 完备度量空间中的混沌判定. 数学学报, 2021, 64(2): 225-230 https://doi.org/10.12386/A2021sxxb0019
Xiao Ying WU, Yuan Long, CHEN Fen WANG. Chaotic Criteria in Complete Metric Spaces. Acta Mathematica Sinica, Chinese Series, 2021, 64(2): 225-230 https://doi.org/10.12386/A2021sxxb0019

参考文献

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基金

国家自然科学基金（11671410，61907010）；广东省自然科学基金（2017A030313037，2018A0303130120）及广东省普通高校自然科学重点项目（2019KZDXM036）
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