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Diffeomorphisms in 1(M) satisfy Axiom A

  • Shuhei Hayashi (a1)
  • DOI:
  • Published online: 01 September 2008

R. Mañé has given a proof of the C1 Stability Conjecture and conjectured that every element of ℱ1(M) satisfies Axiom A. Here we prove that this conjecture is true.

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[1]J. Franks . Necessary conditions for stability of diffeomorphisms. Trans. Amer. Math. Soc. 158 (1971), 301308.

[2]M. Hirsch , C. Pugh & M. Shub . Invariant manifolds. Lecture Notes in Math. 583 (Springer: New York, 1977).

[3]R. Mañé . An ergodic closing lemma. Ann. Math. 116 (1982), 503540.

[4]R. Mañé . On the creation of homoclinic points. Publ. Math. IHES 66 (1988), 139159.

[5]R. Mañé . A proof of the C1 Stability Conjecture. Publ. Math. IHES 66 (1988), 161210.

[6]J. Palis . On the C1 Ω-Stability Conjecture. Publ. Math. IHES 66 (1988), 211215.

[7]S. Smale . Differentiable dynamical systems. Bull. Amer. Math. Soc. 73 (1967), 747817.

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Ergodic Theory and Dynamical Systems
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