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Orbital shadowing property

Bahman Honary|Alireza Zamani Bahabadi
대한수학회 (The Korean Mathematical Society)|2008.11|대한수학회보 (Bulletin of the KMS)|제45권 제4호|pp. 645-650

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참고문헌

키워드

shadowing propertyorbital shadowing propertyδ-pseudo-orbit
주제분류수학

초록

Let M be a generalized homogeneous compact space, and let Z(M) denotes the space of homeomorphisms of M with the C0 topology. In this paper, we show that if the interior of the set of weak stable homeomorphisms on M is not empty then for any open subset W of Z(M) containing only weak stable homeomorphisms the orbital shadowing property is generic in W.

Abstract

Let M be a generalized homogeneous compact space, and let Z(M) denotes the space of homeomorphisms of M with the C0 topology. In this paper, we show that if the interior of the set of weak stable homeomorphisms on M is not empty then for any open subset W of Z(M) containing only weak stable homeomorphisms the orbital shadowing property is generic in W.

참고문헌 (11)

  1. 최태영, "Weak inverse shadowing and genericity", 대한수학회지, 43(1), pp.43~52 (2006), 대한수학회
  2. B. A. Coomes, "Periodic shadowing, Chaotic numerics (Geelong, 1993)", pp.115~130 (1994), Bulletin of the American Mathematical Society
  3. R. M. Corless, "Approximate and real trajectories for generic dynamical systems", Journal of Mathematical Analysis and Applications, 189(2), pp.409~423 (1995)
  4. P. E. Kloeden, "Hyperbolic homeomorphisms and bishadowing", Annales Polonici Mathematici, 65(2), pp.171~177 (1997)
  5. P. Koscielniak, "Chaos and the shadowing property", Topology and its Applications, 154(13), pp.2553~2557 (2007)
  6. K. Kuratowski, "Topology. Vol. II" (1968), Academic Press
  7. M. Mazur, "Weak shadowing for discrete dynamical systems on nonsmooth manifolds", Journal of Mathematical Analysis and Applications, 281(2), pp.657~662 (2003)
  8. M. Mazur, "Tolerance stability conjecture revisited", Topology and its Applications, 131(1), pp.33~38 (2003)
  9. S. Yu. Pilyugin, "Shadowing is generic", Topology and its Applications, 97(3), pp.253~266 (1999)
  10. F. Takens, "On Zeeman’s tolerance stability conjecture", pp.209~219 (1971), Spriger-Verlag
  11. P.Walters, "On the pseudo-orbit tracing property and its relationship to stability", pp.231~244 (1978), Springer

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