弗雷谢特空间上完全元胞群和线性算子的内定态混沌

IF 1.2 3区数学 Q1 MATHEMATICS

Journal of Mathematical Analysis and Applications Pub Date : 2024-11-05 DOI:10.1016/j.jmaa.2024.129033

Zhen Jiang, Jian Li

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引用次数: 0

摘要

利用拓扑动力学的一些技术，我们对完全可元群的连续内定形的Li-Yorke混沌、平均Li-Yorke混沌和分布混沌进行了统一处理，并从所谓半不规则点（或不规则点）的存在角度描述了三种混沌（或极端混沌）。我们列举了一些波兰群内自变的例子来说明这些结果。我们还将我们的结果应用于弗雷谢特空间上连续线性算子的混沌理论，从而改进了文献中的一些结果。

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Chaos for endomorphisms of completely metrizable groups and linear operators on Fréchet spaces

Using some techniques from topological dynamics, we give a uniform treatment of Li-Yorke chaos, mean Li-Yorke chaos and distributional chaos for continuous endomorphisms of completely metrizable groups, and characterize three kinds of chaos (resp. extreme chaos) in terms of the existence of the so-called semi-irregular points (resp. irregular points). We exhibit some examples of inner automorphisms of Polish groups to illustrate the results. We also apply our results to the chaos theory of continuous linear operators on Fréchet spaces, which improves some results in the literature.

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来源期刊

Journal of Mathematical Analysis and Applications 数学-数学

CiteScore

2.50

自引率

7.70%

发文量

790

审稿时长

6 months

期刊介绍： The Journal of Mathematical Analysis and Applications presents papers that treat mathematical analysis and its numerous applications. The journal emphasizes articles devoted to the mathematical treatment of questions arising in physics, chemistry, biology, and engineering, particularly those that stress analytical aspects and novel problems and their solutions. Papers are sought which employ one or more of the following areas of classical analysis: • Analytic number theory • Functional analysis and operator theory • Real and harmonic analysis • Complex analysis • Numerical analysis • Applied mathematics • Partial differential equations • Dynamical systems • Control and Optimization • Probability • Mathematical biology • Combinatorics • Mathematical physics.