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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
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WRAP-statistical-properties-flows-unbounded-roof-function-Lorenz-attractor-2018.pdf - Accepted Version - Requires a PDF viewer. Download (668Kb) | Preview |
Official URL: https://doi.org/10.1007/s10955-018-2093-y
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 | ||||||||||||||||||
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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), Central limit theorem | ||||||||||||||||||
| Journal or Publication Title: | Journal of Statistical Physics | ||||||||||||||||||
| Publisher: | Springer New York LLC | ||||||||||||||||||
| ISSN: | 0022-4715 | ||||||||||||||||||
| Official Date: | August 2018 | ||||||||||||||||||
| Dates: |
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| 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 | ||||||||||||||||||
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