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January  2005, 12(1): 79-96. doi: 10.3934/dcds.2005.12.79

Statistical properties of compact group extensions of hyperbolic flows and their time one maps

Michael Field 1, , Ian Melbourne 2, , Matthew Nicol 1, and  Andrei Török 1,

1. 

Department of Mathematics, University of Houston, Houston, TX 77204-3008, United States, United States
2. 

Department of Mathematics and Statistics, University of Surrey, Guildford, Surrey GU2 7XH, United Kingdom

Received  July 2003 Revised  July 2004 Published  December 2004

Recent work of Dolgopyat shows that "typical" hyperbolic flows exhibit rapid decay of correlations. Melbourne and Török used this result to derive statistical limit laws such as the central limit theorem and the almost sure invariance principle for the time-one map of such flows.
In this paper, we extend these results to equivariant observations on compact group extensions of hyperbolic flows and their time one maps.
Keywords: decay of correlations, almost sure invariance principle, hyperbolic flow, axiom A., Compact group extensions.
Mathematics Subject Classification: 37A25, 37A50, 37D20, 37C8.
Citation: Michael Field, Ian Melbourne, Matthew Nicol, Andrei Török. Statistical properties of compact group extensions of hyperbolic flows and their time one maps. Discrete & Continuous Dynamical Systems, 2005, 12 (1) : 79-96. doi: 10.3934/dcds.2005.12.79
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