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

Michael Field; Ian Melbourne; Matthew Nicol; Andrei Török

doi:10.3934/dcds.2005.12.79

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2005, Volume 12, Issue 1: 79-96. Doi: 10.3934/dcds.2005.12.79

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

1.
Department of Mathematics, University of Houston, Houston, TX 77204-3008
2.
Department of Mathematics and Statistics, University of Surrey, Guildford, Surrey GU2 7XH

Received: June 30, 2003

Revised: June 30, 2004

Published: March 2005

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Abstract

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.

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Mathematics Subject Classification: 37A25, 37A50, 37D20, 37C80.

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