Limit theorems for toral partially hyperbolic endomorphisms
Dynamical Systems
2025-07-21 v2 Probability
Abstract
Under natural assumptions on the observable, we prove a Central Limit Theorem, a Berry-Esseen Theorem, and a quantitative Local Limit Theorem for a broad class of partially hyperbolic endomorphisms of the two-dimensional torus. Our results apply, but are not limited to, skew-products and their perturbations, and they remain valid even when the system admits multiple, though finitely many, absolutely continuous ergodic invariant measures.
Cite
@article{arxiv.2507.05959,
title = {Limit theorems for toral partially hyperbolic endomorphisms},
author = {Roberto Castorrini and Kasun Fernando},
journal= {arXiv preprint arXiv:2507.05959},
year = {2025}
}