Large deviation principles for non-uniformly hyperbolic rational maps

Details Large deviation principles for non-uniformly hyperbolic rational maps Large deviation principles for non-uniformly hyperbolic rational maps

2008-12-27

arxiv.org/abs/0812.4761v2

Mathematics

Dynamical Systems

Final version; to appear in Ergodic Theory and Dynamical Systems

Scientific paper

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.

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