%0 Journal Article
%T Large deviation principles for non-uniformly hyperbolic rational maps
%A Henri Comman
%A Juan Rivera-Letelier
%J Mathematics
%D 2008
%I arXiv
%R 10.1017/S0143385709001163
%X We show some level-2 large deviation principles for rational maps satisfying a strong form of non-uniform hyperbolicity, called "Topological Collet-Eckmann". More precisely, we prove a large deviation principle for the distribution of iterated preimages, periodic points, and Birkhoff averages. For this purpose we show that each H{\"o}lder continuous potential admits a unique equilibrium state, and that the pressure function can be characterized in terms of iterated preimages, periodic points, and Birkhoff averages. Then we use a variant of a general result of Kifer.
%U http://arxiv.org/abs/0812.4761v2