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DOMINATED SPLITTING WITH STABLY EXPANSIVE

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초록

In this paper, we show that if a transitive set ¤ is C1-stably expansive,then ¤ admits a dominated splitting.

Abstract

In this paper, we show that if a transitive set ¤ is C1-stably expansive,then ¤ admits a dominated splitting.

참고문헌 (8)

  1. N. Aoki, "Topological Theory of Dynamical Systems" (1994), North-Holland Math. Library
  2. C. Bonatti, "A C1-generic dichotomy for diffeomorphisms: weak forms of hyperbolicity or infinitely many sinks or sources", Annals of Math, 158, pp.187~222 (2003)
  3. C. Bonatti, "Perturbations of the derivative along periodic orbits", Ergodi. Th. & Dynm. Syst, 26, pp.1307~1337 (2006)
  4. K. Lee, "C1-stably weak shadowing property of chain transitive sets", ~
  5. K. Lee, "Hyperbolicity of C1-stably expansive homoclinic classes", Disc. & Contin. Dynam. Syst, 27, pp.1133~1145 (2010)
  6. R. Mane, "Expansive diffeomorphisms", Lecture Notes in Math, 468, pp.162~174 (1975), Springer-Verlag
  7. R. Mane, "An ergodic closing lemma", Ann. Math, 116, pp.503~540 (1982)
  8. D. Yang, "Stably weakly shadowing transiteve sets and dominated splitting", Proc. Amer. Math. Soc, 통권 : 139, pp.2747~2751 (2011)

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