Statistics of multipliers for hyperbolic rational maps
Dynamical Systems
2020-10-30 v1
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.
Cite
@article{arxiv.2010.15646,
title = {Statistics of multipliers for hyperbolic rational maps},
author = {Richard Sharp and Anastasios Stylianou},
journal= {arXiv preprint arXiv:2010.15646},
year = {2020}
}