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Statistics of multipliers for hyperbolic rational maps
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Sharp, Richard and Stylianou, Anastasios (2021) Statistics of multipliers for hyperbolic rational maps. Discrete and Continuous Dynamical Systems A . (In Press)
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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 | ||||||
|---|---|---|---|---|---|---|---|
| Divisions: | Faculty of Science > Mathematics | ||||||
| Journal or Publication Title: | Discrete and Continuous Dynamical Systems A | ||||||
| Publisher: | American Institute of Mathematical Sciences (AIMS) | ||||||
| ISSN: | 1078-0947 | ||||||
| Official Date: | 2021 | ||||||
| Dates: |
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| Status: | Peer Reviewed | ||||||
| Publication Status: | In Press | ||||||
| Publisher Statement: | 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. The definitive publisher-authenticated version [insert complete citation information here] is available online at: xxxxxxx | ||||||
| Access rights to Published version: | Restricted or Subscription Access | ||||||
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