On Thermodynamics of Rational Maps on the Riemann sphere
Dynamical Systems
2007-05-23 v1 Complex Variables
Abstract
We show that there is a spectral gap for the transfer operator associated to a rational map f on the Riemann sphere. Using this and the method of pertubed operators we establish the (Local) Central Limit Theorem for the measure of maximal entropy of f, with an estimate on the speed of convergence.
Keywords
Cite
@article{arxiv.math/0603507,
title = {On Thermodynamics of Rational Maps on the Riemann sphere},
author = {Tien-Cuong Dinh and Viet-Anh Nguyen and Nessim Sibony},
journal= {arXiv preprint arXiv:math/0603507},
year = {2007}
}
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17 pages