Skip to main content Accessibility help
×
Home

Some open sets of nonuniformly hyperbolic cocycles

Published online by Cambridge University Press:  19 September 2008

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

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
Copyright
Copyright © Cambridge University Press 1993

Access options

Get access to the full version of this content by using one of the access options below.

References

[BC]Benedicks, M. & Carleson, L.. The dynamics of the Hénon map. Ann. Math. 133 (1991), 73169.CrossRefGoogle Scholar
[BY]Benedicks, M. & Young, L.-S.. Sinai-Bowen-Ruelle measures for certain Hénon maps. 1993 Inventiones. To appear.Google Scholar
[F]Furstenberg, H.. Noncommuting random products. Trans. Amer. Math. Soc. 108 (1963), 377428.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), 453502.CrossRefGoogle 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), 469484.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 Unpublished.Google Scholar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), 2758.CrossRefGoogle Scholar
[SS]Sorets, E. & Spencer, T.. Positive Lyapunov exponents for Schrödinger operators with quasiperiodic potentials. Commun. Math. Phys. 142 (1991), 543566.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), 145161.Google Scholar

Full text views

Full text views reflects PDF downloads, PDFs sent to Google Drive, Dropbox and Kindle and HTML full text views.

Total number of HTML views: 0
Total number of PDF views: 24 *
View data table for this chart

* Views captured on Cambridge Core between September 2016 - 20th January 2021. This data will be updated every 24 hours.

Hostname: page-component-76cb886bbf-cdxmh Total loading time: 0.239 Render date: 2021-01-20T01:14:43.895Z Query parameters: { "hasAccess": "0", "openAccess": "0", "isLogged": "0", "lang": "en" } Feature Flags: { "shouldUseShareProductTool": true, "shouldUseHypothesis": true, "isUnsiloEnabled": true, "metricsAbstractViews": false, "figures": false, "newCiteModal": false }

Send article to Kindle

To send this article to your Kindle, first ensure no-reply@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about sending to your Kindle. Find out more about sending to your Kindle.

Note you can select to send to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be sent to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

Find out more about the Kindle Personal Document Service.

Some open sets of nonuniformly hyperbolic cocycles
Available formats
×

Send article to Dropbox

To send this article to your Dropbox account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your <service> account. Find out more about sending content to Dropbox.

Some open sets of nonuniformly hyperbolic cocycles
Available formats
×

Send article to Google Drive

To send this article to your Google Drive account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your <service> account. Find out more about sending content to Google Drive.

Some open sets of nonuniformly hyperbolic cocycles
Available formats
×
×

Reply to: Submit a response


Your details


Conflicting interests

Do you have any conflicting interests? *