Large deviation principles of one-dimensional maps for H\"{o}lder continuous potentials

TL;DR

This paper establishes large deviation principles for one-dimensional maps with weak hyperbolicity, focusing on the distribution of preimages, periodic points, and Birkhoff averages, contributing to the understanding of statistical properties of such dynamical systems.

Contribution

It introduces level-2 large deviation principles for real and complex one-dimensional maps under weak hyperbolicity conditions, extending previous results to broader classes of maps.

Findings

Large deviation principle for iterated preimages

Large deviation principle for periodic points

Large deviation principle for Birkhoff averages

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.