Disc. Cont. Dyn. Syst. 12 (2005) 79-96
Michael Field, Ian Melbourne, Matthew Nicol and Andrew Török
Abstract
Recent work of Dolgopyat shows that ``typical'' hyperbolic flows exhibit rapid decay of correlations. Melbourne and Török 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.