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arXiv · 2507.05959

Limit theorems for toral partially hyperbolic endomorphisms

Roberto Castorrini·Kasun Fernando
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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.

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Roberto Castorrini, Kasun Fernando. 2025-07-08. Limit theorems for toral partially hyperbolic endomorphisms. https://arxiv.org/abs/2507.05959

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