Skip to main content Accessibility help
×
Home

Existence of SRB-measures for some topologically hyperbolic diffeomorphisms

Published online by Cambridge University Press:  09 August 2004

RENAUD LEPLAIDEUR
Affiliation:
Laboratoire de Mathématiques, Université de Bretagne Occidentale, 6 rue Victor Le Gorgeu, BP 809, F-29285 Brest Cedex, France (e-mail: renaud.leplaideur@univ-brest.fr)

Abstract

A diffeomorphism f of a compact manifold M is called almost Axiom-A if it is hyperbolic in a neighborhood of some compact f-invariant set $\Omega$, except in some singular set of neutral points. We prove that if there exists some f-invariant set of hyperbolic points with positive unstable-Lebesgue measure and such that for every point in this set the stable and unstable leaves are ‘long enough’, then f admits either a probability Sinai–Ruelle–Bowen (SRB)-measure or a $\sigma$-finite SRB-measure.

Type
Research Article
Copyright
2004 Cambridge University Press

Access options

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

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: 21 *
View data table for this chart

* Views captured on Cambridge Core between September 2016 - 27th January 2021. This data will be updated every 24 hours.

Hostname: page-component-898fc554b-t4g97 Total loading time: 0.238 Render date: 2021-01-27T17:10:13.671Z 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.

Existence of SRB-measures for some topologically hyperbolic diffeomorphisms
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.

Existence of SRB-measures for some topologically hyperbolic diffeomorphisms
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.

Existence of SRB-measures for some topologically hyperbolic diffeomorphisms
Available formats
×
×

Reply to: Submit a response


Your details


Conflicting interests

Do you have any conflicting interests? *