Journal of the Chungcheong Mathematical Society (충청수학회지)

The Chungcheong Mathematical Society (충청수학회)
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LIMIT SHADOWING WITH $C^0$ TRANSVERSALITY CONDITION

  • Lee, Keonhee (Department of Mathematics Chungnam University) ;
  • Lee, Manseob (Department of Mathematics Mokwon University) ;
  • Park, Junmi (Department of Mathematics Chungnam National University)
  • Published : 2012.05.15
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Abstract

Let $f$ be an Axiom A difeomorphism of a closed 2- dimensional smooth manifold M: We show that $f$ has the limit shadowing property if and only if $f$ satisfies the $C^0$ transversality condition.

Keywords

References

  1. K. Lee, Hyperbolic sets with the strong limit shadowing property, J. of Inequal. Appl. 6 (2001), 507-517.
  2. S. Y. Pilyugin, Shadowing in Dynamical Systems, Lecture Notes Math. 1706, Springer, Berline 1999.
  3. S. Y. Pilyugin, Sets of dynamical systems with various limit shadowing properties, J. Dyn. and Differ. Equat. 19 (2007), 747-775. https://doi.org/10.1007/s10884-007-9073-2
  4. S. Y. Pilyugin and K. Sakai, $C^0$ transversality and shadowing properties, Proc. of the Stek. Inst. Math., 256 (2007), 290-305. https://doi.org/10.1134/S0081543807010178

Cited by

  1. C2-Stably Limit Shadowing Diffeomorphisms vol.2015, 2015, https://doi.org/10.1155/2015/751769