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Statistical properties for flows with unbounded roof function, including the Lorenz attractor

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Bálint, Péter and Melbourne, Ian (2018) Statistical properties for flows with unbounded roof function, including the Lorenz attractor. Journal of Statistical Physics, 172 (4). pp. 1101-1126. doi:10.1007/s10955-018-2093-y ISSN 0022-4715.

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Official URL: https://doi.org/10.1007/s10955-018-2093-y

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Abstract

For geometric Lorenz attractors (including the classical Lorenz attractor) we obtain a greatly simplified proof of the central limit theorem which applies also to the more general class of codimension two singular hyperbolic attractors. We also obtain the functional central limit theorem and moment estimates, as well as iterated versions of these results. A consequence is deterministic homogenisation (convergence to a stochastic differential equation) for fast-slow dynamical systems whenever the fast dynamics is singularly hyperbolic of codimension two.

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), Central limit theorem
Journal or Publication Title: Journal of Statistical Physics
Publisher: Springer New York LLC
ISSN: 0022-4715
Official Date: August 2018
Dates:
DateEvent
August 2018Published
20 June 2018Available
14 June 2018Accepted
Volume: 172
Number: 4
Page Range: pp. 1101-1126
DOI: 10.1007/s10955-018-2093-y
Status: Peer Reviewed
Publication Status: Published
Access rights to Published version: Restricted or Subscription Access
Date of first compliant deposit: 14 June 2018
Date of first compliant Open Access: 20 June 2019
RIOXX Funder/Project Grant:
Project/Grant IDRIOXX Funder NameFunder ID
K104745 Hungarian National Foundation for Scientific Research UNSPECIFIED
K123782Országos Tudományos Kutatási Alapprogramokhttp://dx.doi.org/10.13039/501100003549
K104745 Hungarian National Foundation for Scientific ResearchUNSPECIFIED
K123782Országos Tudományos Kutatási Alapprogramokhttp://dx.doi.org/10.13039/501100003549
ERC AdG 320977European Research Councilhttp://viaf.org/viaf/130022607
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