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SHADOWABLE CHAIN TRANSITIVE SETS OF C1-GENERIC DIFFEOMORPHISMS

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초록

We prove that a locally maximal chain transitive set of a C1-generic diffeomorphism is hyperbolic if and only if it is shadowable.

Abstract

We prove that a locally maximal chain transitive set of a C1-generic diffeomorphism is hyperbolic if and only if it is shadowable.

참고문헌 (11)

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  4. S. Crovisier, "Periodic orbits and chain-transitive sets of C1-diffeomorphisms", Publ. Math. Inst. Hautes Etudes Sci, 104, pp.87~141 (2006)
  5. K. Lee, "Hyperbolicity of C1-stably expansive homoclinic classes", Discrete Contin. Dyn. Syst, 27(3), pp.1133~1145 (2010)
  6. R. Mane, "An ergodic closing lemma", Ann. of Math. (2), 116(3), pp.503~540 (1982)
  7. K. Sakai, "C1-stably shadowable chain components, Ergodic Theory Dynam", Systems, 28(3), pp.987~1029 (2008)
  8. M. Sambarino, "On C1-persistently expansive homoclinic classes", Discrete Contin. Dyn. Syst, 14(3), pp.465~481 (2006)
  9. M. Sambarino, "Robustly expansive homoclinic classes are generically hyperbolic", Discrete Con- tin. Dyn. Syst, 24(4), pp.1325~1333 (2009)
  10. X. Wen, "C1-stably shadowable chain components are hyperbolic", J. Differential Equations, 246(1), pp.340~357 (2009)
  11. D. Yang, "Expansive homoclinic classes", Nonlinearity, 22(4), pp.729~733 (2009)

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