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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 ,
IAN MELBOURNE  and
ANDREW TÖRÖK
MICHAEL FIELD
Affiliation:
Department of Mathematics, University of Houston, Houston, TX 77204-3008, USA (e-mail: [email protected])
IAN MELBOURNE
Affiliation:
Department of Mathematics, University of Houston, Houston, TX 77204-3008, USA (e-mail: [email protected])
ANDREW TÖRÖK
Affiliation:
Department of Mathematics, University of Houston, Houston, TX 77204-3008, USA (e-mail: [email protected]) Institute of Mathematics of the Romanian Academy, PO Box 1–764, RO-70700 Bucharest, Romania
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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
Information
Ergodic Theory and Dynamical Systems , Volume 23 , Issue 1 , February 2003 , pp. 87 - 110
Copyright
2003 Cambridge University Press

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