Large deviation principle in one-dimensional dynamics
Dynamical Systems
2019-07-19 v2 Probability
Abstract
We study the dynamics of smooth interval maps with non-flat critical points. For every such a map that is topologically exact, we establish the full (level-2) Large Deviation Principle for empirical means. In particular, the Large Deviation Principle holds for every non\nobreakdash-renormalizable quadratic map. This includes the maps without physical measure found by Hofbauer and Keller, and challenges the widely-shared view of the Large Deviation Principle as a refinement of laws of large numbers.
Cite
@article{arxiv.1610.00822,
title = {Large deviation principle in one-dimensional dynamics},
author = {Yong Moo Chung and Juan Rivera-Letelier and Hiroki Takahasi},
journal= {arXiv preprint arXiv:1610.00822},
year = {2019}
}
Comments
26 pages, 2 figures, Inventiones mathematicae, to appear