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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
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 | |||||||||||||||
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| 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: |
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| 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: |
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