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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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Official URL: https://doi.org/10.3934/dcds.2021153

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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
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:
DateEvent
March 2022Published
28 October 2021Available
27 August 2021Accepted
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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