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doi: 10.3934/dcds.2021153
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Statistics of multipliers for hyperbolic rational maps
Richard Sharp and Anastasios Stylianou ,
Mathematics Institute, Zeeman Building, University of Warwick, CV4 7AL, Coventry, United Kingdom
Received November 2020 Revised August 2021 Early access October 2021
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.
Keywords: Hyperbolic rational maps, multipliers, holonomy, Julia set, equidistribution, shrinking targets.
Mathematics Subject Classification: 37D20.
Citation: Richard Sharp, Anastasios Stylianou. Statistics of multipliers for hyperbolic rational maps. Discrete & Continuous Dynamical Systems, doi: 10.3934/dcds.2021153
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Richard Sharp Anastasios Stylianou