충청수학회지 (Journal of the Chungcheong Mathematical Society)

  • 제26권2호
  • /
  • Pages.309-313
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  • 2013
  • /
  • 1226-3524(pISSN)
  • /
  • 2383-6245(eISSN)
충청수학회 (The Chungcheong Mathematical Society)
권호 표지
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LINEAR DIFFEOMORPHISMS WITH LIMIT SHADOWING

  • Lee, Keonhee (Department of Mathematics Chungnam University) ;
  • Lee, Manseob (Department of Mathematics Mokwon University) ;
  • Park, Junmi (Department of Mathematics Chungnam National University)
  • 투고 : 2013.01.10
  • 심사 : 2013.04.04
  • 발행 : 2013.05.15
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초록

In this paper, we show that for a linear dynamical system $f(x)=Ax$ of $\mathbb{C}^n$, $f$ has the limit shadowing property if and only if the matrix A is hyperbolic.

키워드

참고문헌

  1. N. Aoki and K. Hiraide, Topological Theory of Dynamical Systems. Recent Advances, North-Holland Math. Library, Vol. 52, North-Holland, Amsterdam, 1994.
  2. K. Lee, Hyperbolic sets with the strong limit shadowing property, J. of Inequal. and Appl. 6 (2001), 507-517.
  3. S. Y. Pilyugin, Shadowing in Dynamical Systems, Lecture Notes in Math. 1706, Springer Verlag, 1999.
  4. S. Y. Pilyugin, A. A. Rodionova, and K. Sakai, Orbital and weak shadowing properties, Discrete Contin. Dynam. Syst. 9 (2003), 287-308.

피인용 문헌

  1. NOTES ON THE EVENTUAL SHADOWING PROPERTY OF A CONTINUOUS MAP vol.30, pp.4, 2017, https://doi.org/10.14403/jcms.2017.30.4.381
  2. Various Shadowing in Linear Dynamical Systems vol.29, pp.3, 2013, https://doi.org/10.1142/s0218127419500421
  3. Shadowing, limit shadowing and two-sided limit shadowing vol.24, pp.5, 2021, https://doi.org/10.1080/09720502.2020.1790745