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Existence and smoothness of the stable foliation for sectional hyperbolic attractors

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Araújo, Vitor and Melbourne, Ian (2017) Existence and smoothness of the stable foliation for sectional hyperbolic attractors. Bulletin of the London Mathematical Society, 49 (2). pp. 351-367. doi:10.1112/blms.12037 ISSN 0024-6093 .

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Official URL: https://doi.org/10.1112/blms.12037

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Abstract

We prove the existence of a contracting invariant topological foliation in a full neighbourhood for partially hyperbolic attractors. Under certain bunching conditions, it can then be shown that this stable foliation is smooth. Specialising to sectional hyperbolic attractors, we give a verifiable condition for bunching. In particular, we show that the stable foliation for the classical Lorenz equation (and nearby vector fields) is better than C1, which is crucial for recent results on exponential decay of correlations. In fact, the foliation is at least C1.278

Item Type: Journal Article
Subjects: Q Science > QA Mathematics
Divisions: Faculty of Science, Engineering and Medicine > Science > Mathematics
Library of Congress Subject Headings (LCSH): Attractors (Mathematics), Lorenz equations, Vector fields
Journal or Publication Title: Bulletin of the London Mathematical Society
Publisher: Oxford University Press
ISSN: 0024-6093
Official Date: April 2017
Dates:
DateEvent
April 2017Published
22 February 2017Available
26 January 2017Valid
26 January 2017Accepted
Volume: 49
Number: 2
Page Range: pp. 351-367
DOI: 10.1112/blms.12037
Status: Peer Reviewed
Publication Status: Published
Reuse Statement (publisher, data, author rights): "This is the peer reviewed version of the following article: Araújo, V. and Melbourne, I. (2017), Existence and smoothness of the stable foliation for sectional hyperbolic attractors. Bull. London Math. Soc., 49: 351-367, which has been published in final form at https://doi.org/10.1112/blms.12037. This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Use of Self-Archived Versions."
Access rights to Published version: Restricted or Subscription Access
Date of first compliant deposit: 30 January 2017
Date of first compliant Open Access: 12 November 2018
RIOXX Funder/Project Grant:
Project/Grant IDRIOXX Funder NameFunder ID
320977European Research Councilhttp://viaf.org/viaf/130022607
313759/2014-6Conselho Nacional de Desenvolvimento Científico e Tecnológicohttp://dx.doi.org/10.13039/501100003593
PRONEX-Dyn.Syst.Conselho Nacional de Desenvolvimento Científico e Tecnológicohttp://dx.doi.org/10.13039/501100003593
UNSPECIFIEDFundação de Amparo à Pesquisa do Estado da Bahiahttp://dx.doi.org/10.13039/501100006181
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