arXiv:0812.4761 Abstract | arXiv Analytics

arXiv:0812.4761 [math.DS]Abstract References Reviews Resources

Large deviation principles for non-uniformly hyperbolic rational maps

Published 2008-12-27, updated 2010-02-06Version 2

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.

Comments: Final version; to appear in Ergodic Theory and Dynamical Systems

Categories: math.DS, math.PR

Subjects: 37D35, 37A50, 37D25, 60F10

Keywords: large deviation principle, non-uniformly hyperbolic rational maps, periodic points, birkhoff averages, iterated preimages

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