Hostname: page-component-78c5997874-m6dg7 Total loading time: 0 Render date: 2024-11-01T07:40:59.865Z Has data issue: false hasContentIssue false

Diffeomorphisms in 1(M) satisfy Axiom A

Published online by Cambridge University Press:  19 September 2008

Shuhei Hayashi
Affiliation:
Department of Mathematics, School of Education, Waseda University, 1-6-1 Nishi-Waseda, Shinjuku, Tokyo 169, Japan

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.

Type
Research Article
Copyright
Copyright © Cambridge University Press 1992

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

[1]Franks, J.. Necessary conditions for stability of diffeomorphisms. Trans. Amer. Math. Soc. 158 (1971), 301308.CrossRefGoogle Scholar
[2]Hirsch, M., Pugh, C. & Shub, M.. Invariant manifolds. Lecture Notes in Math. 583 (Springer: New York, 1977).Google Scholar
[3]Mañé, R.. An ergodic closing lemma. Ann. Math. 116 (1982), 503540.CrossRefGoogle Scholar
[4]Mañé, R.. On the creation of homoclinic points. Publ. Math. IHES 66 (1988), 139159.CrossRefGoogle Scholar
[5]Mañé, R.. A proof of the C 1 Stability Conjecture. Publ. Math. IHES 66 (1988), 161210.CrossRefGoogle Scholar
[6]Palis, J.. On the C 1 Ω-Stability Conjecture. Publ. Math. IHES 66 (1988), 211215.CrossRefGoogle Scholar
[7]Smale, S.. Differentiable dynamical systems. Bull. Amer. Math. Soc. 73 (1967), 747817.CrossRefGoogle Scholar