Statistics of multipliers for hyperbolic rational maps

Richard Sharp; Anastasios Stylianou

doi:10.3934/dcds.2021153

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2022, Volume 42, Issue 3: 1225-1241. 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

^* Corresponding author
^* Corresponding author

Received: November 2020

Revised: August 2021

Early access: October 2021

Published: March 2022

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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.

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Mathematics Subject Classification: 37D20.

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References

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