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http://dx.doi.org/10.4134/JKMS.j190083

EVENTUAL SHADOWING FOR CHAIN TRANSITIVE SETS OF C1 GENERIC DYNAMICAL SYSTEMS  

Lee, Manseob (Department of Marketing Big Data and Mathematics Mokwon University)
Publication Information
Journal of the Korean Mathematical Society / v.58, no.5, 2021 , pp. 1059-1079 More about this Journal
Abstract
We show that given any chain transitive set of a C1 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 C1 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).
Keywords
Shadowing; eventual shadowing; chain transitive; locally maximal; generic; hyperbolic;
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Times Cited By KSCI : 3  (Citation Analysis)
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