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Statistical properties of singular hyperbolic attractors Melbourne, Ian
Description
The classical Lorenz attractor (Lorenz 1963) satisfies various statistical properties such as existence of an SRB measure, central limit theorems, and exponential decay of correlations. The main ingredients are that the attractor is singularly hyperbolic with a $C^r$ stable foliation for some $r>1.$ Certain classes of Lorenz attractors have been obtained analytically for the extended Lorenz equations by Dumortier, Kokubu \& Oka, and more recently by Ovsyannikov \& Turaev. These attractors are singularly hyperbolic but do not have a smooth stable foliation. The aim in this talk (joint work with Vitor Araujo) is to consider statistical properties for singular hyperbolic attractors that do not have a smooth stable foliation. It turns out that existence of an SRB measure, central limit theorems, and mixing hold as in the classical case. But exponential decay of correlations looks currently hopeless. Proving rates of mixing (eg superpolynomial decay) looks perhaps a bit less hopeless
Item Metadata
Title |
Statistical properties of singular hyperbolic attractors
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Creator | |
Publisher |
Banff International Research Station for Mathematical Innovation and Discovery
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Date Issued |
2018-03-23T09:58
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Description |
The classical Lorenz attractor (Lorenz 1963) satisfies various statistical properties such as existence of an SRB measure, central limit theorems, and exponential decay of correlations. The main ingredients are that the attractor is singularly hyperbolic with a $C^r$ stable foliation for some $r>1.$
Certain classes of Lorenz attractors have been obtained analytically for the extended Lorenz equations by Dumortier, Kokubu \& Oka, and more recently by Ovsyannikov \& Turaev. These attractors are singularly hyperbolic but do not have a smooth stable foliation. The aim in this talk (joint work with Vitor Araujo) is to consider statistical properties for singular hyperbolic attractors that do not have a smooth stable foliation. It turns out that existence of an SRB measure, central limit theorems, and mixing hold as in the classical case. But exponential decay of correlations looks currently hopeless. Proving rates of mixing (eg superpolynomial decay) looks perhaps a bit less hopeless
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Extent |
49 minutes
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File Format |
video/mp4
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Language |
eng
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Notes |
Author affiliation: University of Warwick
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Series | |
Date Available |
2018-09-20
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Provider |
Vancouver : University of British Columbia Library
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Rights |
Attribution-NonCommercial-NoDerivatives 4.0 International
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DOI |
10.14288/1.0372097
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URI | |
Affiliation | |
Peer Review Status |
Unreviewed
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Scholarly Level |
Faculty
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Rights URI | |
Aggregated Source Repository |
DSpace
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Rights
Attribution-NonCommercial-NoDerivatives 4.0 International