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June 2017 A Geometric Model of Mixing Lyapunov Exponents Inside Homoclinic Classes in Dimension Three
Xiaolong LI
Tokyo J. Math. 40(1): 1-43 (June 2017). DOI: 10.3836/tjm/1502179213

Abstract

For $C^1$ diffeomorphisms of three dimensional closed manifolds, we provide a geometric model of mixing Lyapunov exponents inside a homoclinic class of a periodic saddle $p$ with non-real eigenvalues. Suppose $p$ has stable index two and the sum of the largest two Lyapunov exponents is greater than $\log(1-\delta)$, then $\delta$-weak contracting eigenvalues are obtained by an arbitrarily small $C^1$ perturbation. Using this result, we give a sufficient condition for stabilizing a homoclinic tangency within a given $C^1$ perturbation range.

Citation

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Xiaolong LI. "A Geometric Model of Mixing Lyapunov Exponents Inside Homoclinic Classes in Dimension Three." Tokyo J. Math. 40 (1) 1 - 43, June 2017. https://doi.org/10.3836/tjm/1502179213

Information

Published: June 2017
First available in Project Euclid: 8 August 2017

zbMATH: 1377.37033
MathSciNet: MR3689976
Digital Object Identifier: 10.3836/tjm/1502179213

Subjects:
Primary: 37C20
Secondary: 37C29, 37D25, 37D30

Rights: Copyright © 2017 Publication Committee for the Tokyo Journal of Mathematics

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Vol.40 • No. 1 • June 2017
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