Ergodic Theory and Dynamical Systems



Decay of correlations, central limit theorems and approximation by Brownian motion for compact Lie group extensions


MICHAEL FIELD a1, IAN MELBOURNE  1 a1 and ANDREW TÖRÖK a1a2
a1 Department of Mathematics, University of Houston, Houston, TX 77204-3008, USA (e-mail: mf@uh.edu)
a2 Institute of Mathematics of the Romanian Academy, PO Box 1–764, RO-70700 Bucharest, Romania

Abstract

Hölder 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 and Pollicott, we obtain similar results for equivariant observations on compact group extensions of hyperbolic basic sets.

(Received March 27 2001)
(Revised January 12 2002)



Footnotes

1 Permanent address: Department of Mathematics and Statistics, University of Surrey, Guildford, Surrey GU2 7XH, UK.