Large deviation principles of one-dimensional maps for Hölder continuous potentials

Abstract

We show some level-2 large deviation principles for real and complex one-dimensional maps satisfying a weak form of hyperbolicity. More precisely, we prove a large deviation principle for the distribution of iterated preimages, periodic points, and Birkhoff averages.

arXiv admin note: text overlap with arXiv:1210.0521

References in corpus (3)

• Large deviations for systems with non-uniform structure
• Pesin theory and equilibrium measures on the interval
• On the asymptotic expansion of maps with disconnected Julia set

Cited by in corpus (2)

• Large deviation principle in one-dimensional dynamics
• Statistical properties of periodic points for infinitely renormalizable unimodal maps