충청수학회지 (Journal of the Chungcheong Mathematical Society)

  • 제26권1호
  • /
  • Pages.45-52
  • /
  • 2013
  • /
  • 1226-3524(pISSN)
  • /
  • 2383-6245(eISSN)
충청수학회 (The Chungcheong Mathematical Society)
권호 표지
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TRANSITIVE SETS WITH C1-STABLY LIMIT SHADOWING

  • Lee, Keonhee (Department of Mathematics Chungnam National University) ;
  • Lee, Manseob (Department of Mathematics Mokwon University) ;
  • Lee, Seunghee (Department of Mathematics Chungnam National University)
  • 투고 : 2012.08.17
  • 심사 : 2013.01.11
  • 발행 : 2013.02.15
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초록

We show that a nontrivial transitive set is $C^1$-stably limit shadowable if and only if the transitive set is hyperbolic.

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참고문헌

  1. K. Lee, Hyperbolic sets with the strong limit shadowing property, J. of Inequal. & Appl. 6 (2001), 507-517.
  2. K. Lee, K. Moriyasu and K. Sakai, $C^1$-stable diffeomorphisms, Discrete and contin. Dynam. Syst. 22 (2008),683-697. https://doi.org/10.3934/dcds.2008.22.683
  3. R. Mane, An ergodic closing lemma, Ann. Math. 116 (1982), 503-540. https://doi.org/10.2307/2007021
  4. S. Y. Pilyugin, "Shadowing in Dynamical Systems.", Lecture Notes in Math. 1706 (Springer Verlag, Berlin, 1999).
  5. C. Pugh, An improved closing lemma and a general density theorem, Amer. J. Math. 89 (1967), 1010-1021. https://doi.org/10.2307/2373414
  6. K. Sakai, Pseudo orbit tracing property and strong transversality of diffeomorphisms on closed manifolds, Osaka J. Math. 31 (1994), 373-386.