Decay of correlations, central limit theorems and approximation by Brownian motion for compact Lie group extensions
- 16 January 2003
- journal article
- research article
- Published by Cambridge University Press (CUP) in Ergodic Theory and Dynamical Systems
- Vol. 23 (01) , 87-110
- https://doi.org/10.1017/s0143385702000901
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.Keywords
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