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Comparison theorems for closed geodesics on negatively curved surfaces
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Pollicott, Mark and Cantrell, Stephen (2022) Comparison theorems for closed geodesics on negatively curved surfaces. Groups, Geometry and Dynamics, 16 (2). pp. 461-491. doi:10.4171/ggd/671 ISSN 1661-7207.
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Official URL: https://doi.org/10.4171/ggd/671
Abstract
In this note we present new asymptotic estimates comparing the word length and geodesic length of closed geodesics on surfaces with (variable) negative sectional curvatures. In particular, we provide an averaged comparison of these two important quantities and obtain precise statistical results, including a central limit theorem and a local limit theorem. Further, as a corollary we also improve an asymptotic formula of R. Sharp and the second author. Finally, we relate our results to recent work of Gekhtman, Taylor and Tiozzo.
| 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): | Differentiable dynamical systems, Hyperbolic groups, Surfaces | |||||||||
| Journal or Publication Title: | Groups, Geometry and Dynamics | |||||||||
| Publisher: | European Mathematical Society Publishing House | |||||||||
| ISSN: | 1661-7207 | |||||||||
| Official Date: | 12 August 2022 | |||||||||
| Dates: |
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| Volume: | 16 | |||||||||
| Number: | 2 | |||||||||
| Page Range: | pp. 461-491 | |||||||||
| DOI: | 10.4171/ggd/671 | |||||||||
| Status: | Peer Reviewed | |||||||||
| Publication Status: | Published | |||||||||
| Access rights to Published version: | Open Access (Creative Commons) | |||||||||
| Copyright Holders: | EMS Press | |||||||||
| Date of first compliant deposit: | 7 March 2022 | |||||||||
| Date of first compliant Open Access: | 21 September 2022 | |||||||||
| RIOXX Funder/Project Grant: |
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