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arXiv · 2509.07657

Wasserstein convergence rates in the invariance principle for nonuniformly hyperbolic flows

Ian Melbourne·Zhe Wang
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Abstract

We obtain $q$-Wasserstein convergence rates in the invariance principle for nonuniformly hyperbolic flows, where $q\ge1$ depends on the degree of nonuniformity. Utilizing a martingale-coboundary decomposition for nonuniformly expanding semiflows, we extend techniques from the discrete-time setting to the continuous-time case. Our results apply to uniformly hyperbolic (Axiom A) flows, nonuniformly hyperbolic flows that can be modelled by suspensions over Young towers with exponential tails (such as dispersing billiard flows and the classical Lorenz attractor), and intermittent solenoidal flows.

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Ian Melbourne, Zhe Wang. 2025-09-09. Wasserstein convergence rates in the invariance principle for nonuniformly hyperbolic flows. https://arxiv.org/abs/2509.07657

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