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Diffeomorphisms in 1(M) satisfy Axiom A

  • Shuhei Hayashi (a1)
Abstract
Abstract

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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References
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[1]Franks J.. Necessary conditions for stability of diffeomorphisms. Trans. Amer. Math. Soc. 158 (1971), 301308.
[2]Hirsch M., Pugh C. & Shub M.. Invariant manifolds. Lecture Notes in Math. 583 (Springer: New York, 1977).
[3]Mañé R.. An ergodic closing lemma. Ann. Math. 116 (1982), 503540.
[4]Mañé R.. On the creation of homoclinic points. Publ. Math. IHES 66 (1988), 139159.
[5]Mañé R.. A proof of the C 1 Stability Conjecture. Publ. Math. IHES 66 (1988), 161210.
[6]Palis J.. On the C 1 Ω-Stability Conjecture. Publ. Math. IHES 66 (1988), 211215.
[7]Smale S.. Differentiable dynamical systems. Bull. Amer. Math. Soc. 73 (1967), 747817.
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Ergodic Theory and Dynamical Systems
  • ISSN: 0143-3857
  • EISSN: 1469-4417
  • URL: /core/journals/ergodic-theory-and-dynamical-systems
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