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

Published online by Cambridge University Press:  16 January 2003

MICHAEL FIELD
Affiliation:
Department of Mathematics, University of Houston, Houston, TX 77204-3008, USA (e-mail: mf@uh.edu)
IAN MELBOURNE
Affiliation:
Department of Mathematics, University of Houston, Houston, TX 77204-3008, USA (e-mail: mf@uh.edu)
ANDREW TÖRÖK
Affiliation:
Department of Mathematics, University of Houston, Houston, TX 77204-3008, USA (e-mail: mf@uh.edu) 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.

Type
Research Article
Copyright
2003 Cambridge University Press

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