충청수학회지 (Journal of the Chungcheong Mathematical Society)

  • 제29권1호
  • /
  • Pages.151-155
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  • 2016
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  • 1226-3524(pISSN)
  • /
  • 2383-6245(eISSN)
충청수학회 (The Chungcheong Mathematical Society)
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CONTINUUM-WISE EXPANSIVE HOMEOMORPHISMS WITH SHADOWING

  • Lee, Keonhee (Department of Mathematics, Chungnam University) ;
  • Lee, Seunghee (Department of Mathematics, Chungnam University)
  • 투고 : 2016.01.08
  • 심사 : 2016.02.05
  • 발행 : 2016.02.15
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초록

In this paper, we show that if a continuum-wise expansive homeomorphism on a compact connected metric space is shadowing then it is topologically stable. This generalizes the main result of [4].

키워드

참고문헌

  1. A. Artigue and D. Carrasco-Olivera, A note on measure-expansive diffeomorphisms, preprint.
  2. J. R. Hertz, There are no stable points for continuum-wise expansive homeomorphisms, preprint.
  3. H. Kato, Continuum-wise expansive homeomorphisms, Canad. J. Math. 45 (1993), no. 3, 576-598. https://doi.org/10.4153/CJM-1993-030-4
  4. P. Walters, On the pseudo orbits tracing property and its relationship to stability, 231-244, Lecture Notes in Math. 668, Springer-Verlag, Berlin (1977).