Journal of the Chungcheong Mathematical Society (충청수학회지)

The Chungcheong Mathematical Society (충청수학회)
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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)
  • Received : 2013.01.10
  • Accepted : 2013.04.04
  • Published : 2013.05.15
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Abstract

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.

Keywords

References

  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.

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  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