  We present the first rates of convergence to an $N$-dimensional Brownian
motion when $N\ge2$ for discrete and continuous time dynamical systems.
Additionally, we provide the first rates for continuous time in any dimension.
Our results hold for nonuniformly hyperbolic and expanding systems, such as
Axiom A flows, suspensions over a Young tower with exponential tails, and some
classes of intermittent solenoids.
