Continuum-wise expansiveness for discrete dynamical systems

被引：0
|
作者：
Lee, Manseob [1 ]
机构：
[1] Mokwon Univ, Dept Mkt Big Data & Math, Daejeon 302729, South Korea
来源：
REVISTA DE LA REAL ACADEMIA DE CIENCIAS EXACTAS FISICAS Y NATURALES SERIE A-MATEMATICAS | 2021年 / 115卷 / 03期
关键词：
Expansive; Continuum-wise expansive; Transitive set; Hyperbolic; HOMOCLINIC CLASSES; HYPERBOLICITY; STABILITY; ROBUST;
D O I：
10.1007/s13398-021-01056-w
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
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 C-1 stably continuum-wise expansive then it is hyperbolic. These results generalize those of Mane (Topology 17:383-396, 1978) and Lee and Park (Dyn Syst 33:228-238, 2018).
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页数：11
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