Limit Theorem for Partially Hyperbolic Endomorphisms
Abstract: In this talk, I will present recent results obtained in collaboration with Roberto Castorrini (SNS, Pisa). 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.