충청수학회지 (Journal of the Chungcheong Mathematical Society)

  • 제25권1호
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  • Pages.27-33
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  • 2012
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  • 1226-3524(pISSN)
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  • 2383-6245(eISSN)
충청수학회 (The Chungcheong Mathematical Society)
권호 표지
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ASYMPTOTIC AVERAGE SHADOWING PROPERTY ON A CLOSED SET

  • Lee, Manseob (Department of Mathematics Mokwon University) ;
  • Park, Junmi (Department of Mathematics Chungnam National University)
  • 발행 : 2012.02.15
⟨ 이전 논문 다음 논문 ⟩

초록

Let $f$ be a difeomorphism of a closed $n$ -dimensional smooth manifold M, and $p$ be a hyperbolic periodic point of $f$. Let ${\Lambda}(p)$ be a closed set which containing $p$. In this paper, we show that (i) if $f$ has the asymptotic average shadowing property on ${\Lambda}(p)$, then ${\Lambda}(p)$ is the chain component which contains $p$. (ii) suppose $f$ has the asymptotic average shadowing property on ${\Lambda}(p)$. Then if $f|_{\Lambda(p)}$ has the $C^{1}$-stably shadowing property then it is hyperbolic.

키워드

참고문헌

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  6. K. Lee and X. Wen, Shadowable chain transitive sets of $C^{1}$-generic diffeomorphisms, preprint.
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  8. X. Wen, S. Gan and L. Wen, $C^{1}$-stably shadowable chain components are hyperbolic, J. Diff. Equa. 246 (2009), 340-357. https://doi.org/10.1016/j.jde.2008.03.032