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The local star condition for generic transitive diffeomorphisms

Manseob Lee
대한수학회 (The Korean Mathematical Society)|2016.04|대한수학회논문집 (Communications of the KMS)|제31권 제2호|pp. 389-394

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참고문헌

키워드

hyperbolictransitive setstar diffeomorphismslocal star diffeomorphisms
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초록

Let $f:M\to M$ be a diffeomorphism on a closed $C^{\infty}$ $d(\geq2)$ 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.

Abstract

Let $f:M\to M$ be a diffeomorphism on a closed $C^{\infty}$ $d(\geq2)$ 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.

참고문헌 (9)

  1. F. Abdenur, "Nonuniform hyperbolicity for C1-generic diffeomorphisms", Israel J. Math, 183, pp.1~60 (2011)
  2. N. Aoki, "The set of Axiom A diffeomorphisms with no cycles", Bol. Soc. Brasil. Mat. (N.S.), 23(1-2), pp.21~65 (1992)
  3. S. Hayashi, "Diffeomorphisms in F1(M) satisfy Axiom A", Ergodic Theory Dynam. Systems, 12(2), pp.233~253 (1992)
  4. 이건희, "SHADOWABLE CHAIN TRANSITIVE SETS OF C1-GENERIC DIFFEOMORPHISMS", 대한수학회보, 49(2), pp.263~270 (2012), 대한수학회
  5. R. Mane, "Contributions to the stability conjecture", Topology, 17(4), pp.383~396 (1978)
  6. R. Mane, "An ergodic closing lemma", Ann of Math, 116(3), pp.503~540 (1982)
  7. R. Mane, "A proof of the C1 stability conjecture", Inst. Hautes Etudes Sci. Publ. Math, (66), pp.161~210 (1988)
  8. C. Robinson, "Structural stability of C1-diffeomorphisms", J. Differential Equations, 22(1), pp.28~73 (1976)
  9. W. Sun, "Diffeomorphisms with various C1-stalbe properties", Acta Math. Sci. Ser. B Engl. Ed, 32(2), pp.552~558 (2012)

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