Young structures for partially hyperbolic systems with mostly contracting central direction
Abstract
We establish the existence of Young structures for a broad class of partially hyperbolic diffeomorphisms with a splitting , 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.
Cite
@article{arxiv.2503.21429,
title = {Young structures for partially hyperbolic systems with mostly contracting central direction},
author = {José F. Alves and João S. Matias},
journal= {arXiv preprint arXiv:2503.21429},
year = {2025}
}
Comments
For the algorithm to work, we must ensure that the points used as bases for the rectangles R(z_i) (defined at the beginning of Section 5) have long stable manifolds and are mapped to points with long stable manifolds whenever a return occurs -- something that is not always guaranteed under the return defined in Section 5.1