Fluctuations of ergodic sums on periodic orbits under specification
Dynamical Systems
2020-05-14 v2
Abstract
We study the fluctuations of ergodic sums using global and local specifications on periodic points. We obtain Lindeberg-type central limit theorems in both situations. As an application, when the system possesses a unique measure of maximal entropy, we show weak convergence of ergodic sums to a mixture of normal distributions. Our results suggest decomposing the variances of ergodic sums according to global and local sources.
Keywords
Cite
@article{arxiv.1805.01973,
title = {Fluctuations of ergodic sums on periodic orbits under specification},
author = {Manfred Denker and Samuel Senti and Xuan Zhang},
journal= {arXiv preprint arXiv:1805.01973},
year = {2020}
}