Continuum-wise expansiveness for discrete dynamical systems

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作者
Manseob Lee
机构
[1] Mokwon University,Department of Marketing Big Data and Mathematics
关键词
Expansive; Continuum-wise expansive; Transitive set; Hyperbolic; 37D20; 34D10;
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摘要
In the paper, we will prove that if a continuum-wise expansive homeomorphism f of a compact connected metric space X has a local product structure then it has a periodic point. Moreover, if a nontrivial transitive set of a diffeomorphism f of a compact smooth Riemannian manifold M is C1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$C^1$$\end{document} stably continuum-wise expansive then it is hyperbolic. These results generalize those of Mañé (Topology 17:383–396, 1978) and Lee and Park (Dyn Syst 33:228–238, 2018).
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