Statistical properties of compact group extensions of Hyperbolic flows and their time one maps
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.