Rates of convergence in the multivariate weak invariance principle for nonuniformly hyperbolic maps
Abstract
We obtain rates of convergence in the weak invariance principle for R d \mathbb {R}^d -valued Hölder observables over nonuniformly hyperbolic maps. In particular, for maps modelled by a Young tower with superpolynomial tails (e.g. the Sinai billiard map, and Axiom A diffeomorphisms) we obtain a rate of O ( n − r ) O(n^{-r}) in the Wasserstein p p -metric for all r > 1 / 4 r>1/4 and p > ∞ p>\infty . Additionally, this is the first result on rates that covers certain invertible, slowly mixing maps, such as Bunimovich flowers.
Fields of Study & Subjects
Mathematical Dynamics and Fractals
Quantum chaos and dynamical systems
Advanced Mathematical Modeling in Engineering
Publication details
- Journal / source
- Proceedings of the American Mathematical Society
- Volume
- 154
- Issue
- 5
- Pages
- 2115–2130
- Publication date
- 14 January 2026
- Language
- EN