arXiv subjects

João S. Matias

Publications and source records attributed to João S. Matias.

3 recordsLinked to original sources

arXiv2026

Martingale Methods for Maximal Large Deviations and Young Towers

We develop a martingale approximation framework yielding quantitative maximal large deviations estimates for invertible dynamical systems. From suitable decay of correlations, we deduce these estimates and, as an application, we obtain Young structures with matching recurrence tails for partially hyperbolic diffeomorphisms with mostly expanding central direction. In a second application, we prove maximal large deviation estimates for systems modelled by Young towers with subexponential contraction and expansion. Many examples of slowly mixing billiards are covered by this result.

math.DS↗

arXiv2025

From decay of correlations to recurrence times in systems with contracting directions

Classic results by L.-S. Young show that the decay of correlations for systems that admit inducing schemes can be obtained through the recurrence rates of the inducing scheme. Reciprocal results were obtained for non-invertible systems (without contracting directions). Here, we obtain reciprocal results also for invertible systems (with contracting directions).

math.DS↗

arXiv2025

Young structures for partially hyperbolic systems with mostly contracting central direction

We establish the existence of Young structures for a broad class of partially hyperbolic diffeomorphisms with a splitting $TM = E^{cs} \oplus E^{uu}$, under exactly the same conditions that ensure the existence of SRB measures in a previous work by Bonatti and Viana. This extends the applicability of statistical techniques to systems where statistical properties remained largely unexplored. Our approach refines previous methods, introducing key adaptations to the partially hyperbolic setting. These results provide a foundation for obtaining decay of correlations, Central Limit Theorem, large deviations and a vector-valued almost sure invariance principle in this class of dynamical systems.

math.DS↗