EVENTUAL SHADOWING FOR CHAIN TRANSITIVE SETS OF C1 GENERIC DYNAMICAL SYSTEMS

被引:2
作者
Lee, Manseob [1 ]
机构
[1] Mokwon Univ, Dept Mkt Big Data & Math, Daejeon 35349, South Korea
关键词
Shadowing; eventual shadowing; chain transitive; locally maximal; generic; hyperbolic; PERIODIC-ORBITS; SPECIFICATION; STABILITY; PROPERTY; ROBUST; DIFFEOMORPHISMS; COMPONENTS;
D O I
10.4134/JKMS.j190083
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
We show that given any chain transitive set of a C-1 generic diffeomorphism f, if a diffeomorphism f has the eventual shadowing property on the locally maximal chain transitive set, then it is hyperbolic. Moreover, given any chain transitive set of a C-1 generic vector field X, if a vector field X has the eventual shadowing property on the locally maximal chain transitive set, then the chain transitive set does not contain a singular point and it is hyperbolic. We apply our results to conservative systems (volume-preserving diffeomorphisms and divergence-free vector fields).
引用
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页码:1059 / 1079
页数:21
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