Journal of the Chungcheong Mathematical Society (충청수학회지)

The Chungcheong Mathematical Society (충청수학회)
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GENERIC DIFFEOMORPHISM WITH SHADOWING PROPERTY ON TRANSITIVE SETS

  • Lee, Manseob (Department of Mathematics Mokwon University) ;
  • Kang, Bowon (Department of Mathematics Mokwon University) ;
  • Oh, Jumi (Department of Mathematics Chungnam University)
  • Published : 2012.11.15
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Abstract

Let $f\;:\;M\;{\rightarrow}\;M$ be a diffeomorphism on a closed $C^{\infty}$ manifold. Let $\Lambda$ be a transitive set. In this paper, we show that (i) $C^1$-generically, $f$ has the shadowing property on a locally maximal $\Lambda$ if and only if $\Lambda$ is hyperbolic, (ii) f has the $C^1$-stably shadowing property on $\Lambda$ if and only if $\Lambda$ is hyperbolic.

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References

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Cited by

  1. The ergodic shadowing property and homoclinic classes vol.2014, pp.1, 2014, https://doi.org/10.1186/1029-242X-2014-90