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Some open sets of nonuniformly hyperbolic cocycles

Published online by Cambridge University Press:  19 September 2008

L.-S. Young
L.-S. Young
Affiliation:
Department of Mathematics, UCLA, Los Angeles, CA 90024, USA
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Abstract

We consider some very simple examples of SL(2, ℝ)-cocycles and prove that they have positive Lyapunov exponents. These cocycles form an open set in the C1 topology.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 13 , Issue 2 , June 1993 , pp. 409 - 415
Copyright
Copyright © Cambridge University Press 1993

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References

REFERENCES

[BC]Benedicks, M. & Carleson, L.. The dynamics of the Hénon map. Ann. Math. 133 (1991), 73–169.Google Scholar
[BY]Benedicks, M. & Young, L.-S.. Sinai-Bowen-Ruelle measures for certain Hénon maps. 1993 Inventiones. To appear.CrossRefGoogle Scholar
[F]Furstenberg, H.. Noncommuting random products. Trans. Amer. Math. Soc. 108 (1963), 377–428.CrossRefGoogle Scholar
[H]Herman, M.. Une méthode pour minorer les exposants de Lyapunov et quelques exemples montrant le caractère local d'un theorème d'Arnold et de Moser sur le tore en dimension 2. Commun. Math. Helv. 58 (1983), 453–502.Google Scholar
[K]Knill, O.. Positive Lyapunov exponents for a dense set of bounded measurable Sl(2, ℝ) cocycles. Ergod. Th. & Dynam. Sys. (1992).CrossRefGoogle Scholar
[LY]Ledrappier, F. & Young, L.-S.. Stability of Lyapunov exponents. Ergod. Th. & Dynam. Sys. 11 (1991), 469–484.CrossRefGoogle Scholar
[M]Mañé, R.. The Lyapunov exponents of generic area preserving diffeomorphisms. Unpublished.Google Scholar
[R]Ruelle, D.. Ergodic theory of differentiable dynamical systems. Publ. Math. IHES 50 (1979), 27–58.Google Scholar
[SS]Sorets, E. & Spencer, T.. Positive Lyapunov exponents for Schrödinger operators with quasiperiodic potentials. Commun. Math. Phys. 142 (1991), 543–566.CrossRefGoogle Scholar
[S]Spencer, T.. Ergodic Schrödinger operators. Analysis, et cetera, eds, Rabinowitz, P. and Zehnder, E.. Academic, New York, 1990.Google Scholar
[W]Wojtkowski, M.. Invariant families of cones and Lyapunov exponents. Ergod. Th. & Dynam. Sys. 5(1985), 145–161.Google Scholar