충청수학회지 (Journal of the Chungcheong Mathematical Society)

  • 제24권4호
  • /
  • Pages.631-638
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  • 2011
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  • 1226-3524(pISSN)
  • /
  • 2383-6245(eISSN)
충청수학회 (The Chungcheong Mathematical Society)
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DIFFEOMORPHISMS WITH ROBUSTLY AVERAGE SHADOWING

  • Lee, Keonhee (Department of Mathematics Chungnam University) ;
  • Lee, Manseob (Department of Mathematics Mokwon University) ;
  • Lu, Gang (Department of Mathematics Chungnam University)
  • 투고 : 2011.03.03
  • 심사 : 2011.10.10
  • 발행 : 2011.12.30
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초록

In this paper, we prove that for $C^1$ generically, if every hyperbolic periodic point in a chain component is uniformly far away from being nonhyperbolic, and it is $C^1$-robustly average shadowable, then the chain component is hyperbolic.

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과제정보

연구 과제 주관 기관 : National Research Foundation of Korea(NRF)

참고문헌

  1. C. Bonatti and S. Crovisier, Recurrence and genericity, Invent. Math. 158 (2004), 33-104.
  2. M. Hurley, Bifurcation and chain recurrence, Ergodic Thoery & Dynam. Syst. 3 (1983), 231-240.
  3. M. Lee, Stably average shadowabe homoclinic classes, Nonlinear Anal.: Theory, Methods & Appl. 74 (2011), 689-694. https://doi.org/10.1016/j.na.2010.09.027
  4. R. Mane, An ergodic closing lemma, Ann. Math. 116 (1982), 503-540. https://doi.org/10.2307/2007021
  5. X. Wen, S. Gan and L. Wen, $C^{1}$-stably shadowble chain components are hyper-bolic, J. Differen. Equat. 246 (2009) 340-357. 159-175. https://doi.org/10.1016/j.jde.2008.03.032