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Explicit coupling argument for nonuniformly hyperbolic transformations
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Korepanov, Alexey, Kosloff, Zemer and Melbourne, Ian (2019) Explicit coupling argument for nonuniformly hyperbolic transformations. Proceedings of the Royal Society of Edinburgh Section A : Mathematics, 149 (1). pp. 101-130. doi:10.1017/S0308210518000161 ISSN 0308-2105.
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Official URL: https://doi.org/10.1017/S0308210518000161
Abstract
The transfer operator corresponding to a uniformly expanding map enjoys good spectral properties. We verify that coupling yields explicit estimates that depend continuously on the expansion and distortion constants of the map. For non-uniformly expanding maps with a uniformly expanding induced map, we obtain explicit estimates for mixing rates (exponential, stretched exponential, polynomial) that again depend continuously on the constants for the induced map together with data associated with the inducing time. Finally, for non-uniformly hyperbolic transformations, we obtain the corresponding estimates for rates of decay of correlations.
Item Type: | Journal Article | ||||||||
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Subjects: | Q Science > QA Mathematics | ||||||||
Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||||||
Journal or Publication Title: | Proceedings of the Royal Society of Edinburgh Section A : Mathematics | ||||||||
Publisher: | Cambridge University Press | ||||||||
ISSN: | 0308-2105 | ||||||||
Official Date: | February 2019 | ||||||||
Dates: |
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Volume: | 149 | ||||||||
Number: | 1 | ||||||||
Page Range: | pp. 101-130 | ||||||||
DOI: | 10.1017/S0308210518000161 | ||||||||
Status: | Peer Reviewed | ||||||||
Publication Status: | Published | ||||||||
Access rights to Published version: | Restricted or Subscription Access | ||||||||
Date of first compliant deposit: | 1 December 2016 | ||||||||
Date of first compliant Open Access: | 26 September 2018 |
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