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A central limit theorem for periodic orbits of hyperbolic flows
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Cantrell, Stephen and Sharp, Richard (2021) A central limit theorem for periodic orbits of hyperbolic flows. Dynamical Systems, 36 (1). pp. 142-153. doi:10.1080/14689367.2020.1849030 ISSN 1468-9367.
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WRAP-A-central-limit-theorem-periodic-orbits-hyperbolic-flows-Sharp-2020.pdf - Accepted Version - Requires a PDF viewer. Download (827Kb) | Preview |
Official URL: https://doi.org/10.1080/14689367.2020.1849030
Abstract
We consider a counting problem in the setting of hyperbolic dynamics. Let ϕt:Λ→Λ be a weak-mixing hyperbolic flow. We count the proportion of prime periodic orbits of ϕt, with length less than T, that satisfy an averaging condition related to a Hölder continuous function f:Λ→R. We show, assuming an approximability condition on ϕ, that as T→∞, we obtain a central limit theorem. The proof uses transfer operator estimates due to Dolgopyat to provide the bounds on complex functions that we need to carry out our analysis. We can then use contour integration to obtain the asymptotic behaviour which gives the central limit theorem.
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): | Differential equations, Hyperbolic, Central limit theorem, Combinatorial dynamics | ||||||||
Journal or Publication Title: | Dynamical Systems | ||||||||
Publisher: | Taylor & Francis Ltd. | ||||||||
ISSN: | 1468-9367 | ||||||||
Official Date: | 2021 | ||||||||
Dates: |
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Volume: | 36 | ||||||||
Number: | 1 | ||||||||
Page Range: | pp. 142-153 | ||||||||
DOI: | 10.1080/14689367.2020.1849030 | ||||||||
Status: | Peer Reviewed | ||||||||
Publication Status: | Published | ||||||||
Reuse Statement (publisher, data, author rights): | This is an Accepted Manuscript of an article published by Taylor & Francis in Dynamical Systems on 07/01/2021, available online: http://www.tandfonline.com/10.1080/14689367.2020.1849030 | ||||||||
Access rights to Published version: | Restricted or Subscription Access | ||||||||
Date of first compliant deposit: | 11 November 2020 | ||||||||
Date of first compliant Open Access: | 7 January 2022 | ||||||||
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