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A quantitative version of the Kupka-Smale theorem

Published online by Cambridge University Press:  19 September 2008

Y. Yomdin
Y. Yomdin
Affiliation:
Ben Gurion University of the Negev, Beer-Sheva 84120, Israel
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Abstract

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Let Mm be a compact, m-dimensional smooth manifold. The n-periodic point x of a diffeomorphism f: M → M is called γ-hyperbolic, for γ≥O, if the eigenvalues λj, of dfn(x) satisfy . We prove that any Ck-diffeomorphism f: M → M, k≥3, for any ε>0 can be ε-approximated in Ck-norm by fe: M → M such that for any n each n-periodic point of fe is (a(ε))nα - hyperbolic. Here and ao>0 depends on f

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 5 , Issue 3 , September 1985 , pp. 449 - 472
Copyright
Copyright © Cambridge University Press 1985

References

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