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Statistics of multipliers for hyperbolic rational maps
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Sharp, Richard and Stylianou, Anastasios (2022) Statistics of multipliers for hyperbolic rational maps. Discrete and Continuous Dynamical Systems A, 42 (3). pp. 1225-1241. doi:10.3934/dcds.2021153 ISSN 1078-0947.
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WRAP-statistics-multipliers-hyperbolic-rational-maps-Sharp-2021.pdf - Accepted Version - Requires a PDF viewer. Download (884Kb) | Preview |
Official URL: https://doi.org/10.3934/dcds.2021153
Abstract
In this article, we consider a counting problem for orbits of hyperbolic rational maps on the Riemann sphere, where constraints are placed on the multipliers of orbits. Using arguments from work of Dolgopyat, we consider varying and potentially shrinking intervals, and obtain a result which resembles a local central limit theorem for the logarithm of the absolute value of the multiplier and an equidistribution theorem for the holonomies.
| 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): | Conformal mapping, Geometry, Hyperbolic, Hyperbolic spaces | ||||||||
| Journal or Publication Title: | Discrete and Continuous Dynamical Systems A | ||||||||
| Publisher: | American Institute of Mathematical Sciences (AIMS) | ||||||||
| ISSN: | 1078-0947 | ||||||||
| Official Date: | March 2022 | ||||||||
| Dates: |
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| Volume: | 42 | ||||||||
| Number: | 3 | ||||||||
| Page Range: | pp. 1225-1241 | ||||||||
| DOI: | 10.3934/dcds.2021153 | ||||||||
| Status: | Peer Reviewed | ||||||||
| Publication Status: | Published | ||||||||
| Reuse Statement (publisher, data, author rights): | This is a pre-copy-editing, author-produced PDF of an article accepted for publication in Discrete and Continuous Dynamical Systems A following peer review. Sharp, Richard and Stylianou, Anastasios (2021) Statistics of multipliers for hyperbolic rational maps. Discrete and Continuous Dynamical Systems A is available online at: https://doi.org/10.3934/dcds.2021153 | ||||||||
| Access rights to Published version: | Open Access (Creative Commons) | ||||||||
| Date of first compliant deposit: | 2 September 2021 | ||||||||
| Date of first compliant Open Access: | 28 October 2022 | ||||||||
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