Recent work of Dolgopyat shows that
'typical' hyperbolic flows exhibit rapid decay of
correlations. Melbourne and Torok used this result to derive
statistical limit laws such as the central limit theorem and the almost
sure invariance principle for the time-one map of such flows.
In this paper, we extend these results to equivariant observations
on compact group extensions of hyperbolic flows and their time one maps.
For preprint,
email: mikefield@gmail.com