Holder continuous observations on hyperbolic basic sets satisfy strong statistical properties such as exponential decay of correlations, central limit theorems and invariance principles (approximation by Brownian motion).

Using an equivariant version of the Ruelle transfer operator studied by Parry & Pollicott, we obtain similar results for equivariant observations on compact group extensions of hyperbolic basic sets.

For preprint, e-mail: mikefield@gmail.com

Professor Mike Field
Department of Mathematics
Imperial College
London SW7 2AZ