Large deviation principles for non-uniformly hyperbolic rational maps

Abstract

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{ö}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.

Final version; to appear in Ergodic Theory and Dynamical Systems

References in corpus (2)

• Dynamics in several complex variables: endomorphisms of projective spaces and polynomial-like mapping
• Strengthened large deviations for rational maps and full shifts, with unified proof

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