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Mixing properties and statistical limit theorems for singular hyperbolic flows without a smooth stable foliation
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Araújo, V. and Melbourne, Ian (2019) Mixing properties and statistical limit theorems for singular hyperbolic flows without a smooth stable foliation. Advances in Mathematics, 349 . pp. 212-245. doi:10.1016/j.aim.2019.04.007 ISSN 0001-8708.
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Official URL: https://doi.org/10.1016/j.aim.2019.04.007
Abstract
Over the last 10 years or so, advanced statistical properties, including exponential decay of correlations, have been established for certain classes of singular hyperbolic flows in three dimensions. The results apply in particular to the classical Lorenz attractor. However, many of the proofs rely heavily on the smoothness of the stable foliation for the flow.
In this paper, we show that many statistical properties hold for singular hyperbolic flows with no smoothness assumption on the stable foliation. These properties include existence of SRB measures, central limit theorems and associated invariance principles, as well as results on mixing and rates of mixing. The properties hold equally for singular hyperbolic flows in higher dimensions provided the center-unstable subspaces are two-dimensional.
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) | |||||||||||||||
Journal or Publication Title: | Advances in Mathematics | |||||||||||||||
Publisher: | Academic Press | |||||||||||||||
ISSN: | 0001-8708 | |||||||||||||||
Official Date: | 20 June 2019 | |||||||||||||||
Dates: |
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Volume: | 349 | |||||||||||||||
Page Range: | pp. 212-245 | |||||||||||||||
DOI: | 10.1016/j.aim.2019.04.007 | |||||||||||||||
Status: | Peer Reviewed | |||||||||||||||
Publication Status: | Published | |||||||||||||||
Access rights to Published version: | Restricted or Subscription Access | |||||||||||||||
Date of first compliant deposit: | 4 April 2019 | |||||||||||||||
Date of first compliant Open Access: | 12 April 2020 | |||||||||||||||
RIOXX Funder/Project Grant: |
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