Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
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EVENTUAL SHADOWING FOR CHAIN TRANSITIVE SETS OF C1 GENERIC DYNAMICAL SYSTEMS

  • Lee, Manseob (Department of Marketing Big Data and Mathematics Mokwon University)
  • Received : 2019.01.28
  • Accepted : 2021.01.22
  • Published : 2021.09.01
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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

Acknowledgement

The author wish to express their appreciation to reviewers for their valuable comments.

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