DOI QR코드

DOI QR Code

THE LOCAL STAR CONDITION FOR GENERIC TRANSITIVE DIFFEOMORPHISMS

  • Lee, Manseob (Department of Mathematics Mokwon University)
  • 투고 : 2015.03.18
  • 발행 : 2016.04.30

초록

Let $f:M{\rightarrow}M$ be a diffeomorphism on a closed $C^{\infty}\;d({\geq}2)$ dimensional manifold M. For $C^1$-generic f, if a diffeomorphism f satisfies the local star condition on a transitive set, then it is hyperbolic.

키워드

참고문헌

  1. F. Abdenur, C. Bonatti, and S. Crovisier, Nonuniform hyperbolicity for $C^1$-generic diffeomorphisms, Israel J. Math. 183 (2011), 1-60. https://doi.org/10.1007/s11856-011-0041-5
  2. N. Aoki, The set of Axiom A diffeomorphisms with no cycles, Bol. Soc. Brasil. Mat. (N.S.) 23 (1992), no. 1-2, 21-65. https://doi.org/10.1007/BF02584810
  3. S. Hayashi, Diffeomorphisms in $F^1$(M) satisfy Axiom A, Ergodic Theory Dynam. Systems 12 (1992), no. 2, 233-253.
  4. K. Lee and X. Wen, Shadowable chain transitive sets of $C^1$-generic diffeomorphisms, Bull. Korean Math. Soc. 49 (2012), no. 2, 263-270. https://doi.org/10.4134/BKMS.2012.49.2.263
  5. R. Mane, Contributions to the stability conjecture, Topology 17 (1978), no. 4, 383-396. https://doi.org/10.1016/0040-9383(78)90005-8
  6. R. Mane, An ergodic closing lemma, Ann of Math. 116 (1982), no. 3, 503-540. https://doi.org/10.2307/2007021
  7. R. Mane, A proof of the $C^1$ stability conjecture, Inst. Hautes etudes Sci. Publ. Math. No. 66 (1988), 161-210.
  8. C. Robinson, Structural stability of $C^1$-diffeomorphisms, J. Differential Equations 22 (1976), no. 1, 28-73. https://doi.org/10.1016/0022-0396(76)90004-8
  9. W. Sun and X. Tian, Diffeomorphisms with various $C^1$-stalbe properties, Acta Math. Sci. Ser. B Engl. Ed. 32 (2012), no. 2, 552-558.