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Statistical properties of a skew product with a curve of neutral points

Published online by Cambridge University Press:  28 November 2006

SÉBASTIEN GOUËZEL
SÉBASTIEN GOUËZEL
Affiliation:
IRMAR, Université de Rennes 1, Campus de Beaulieu, 35042 Rennes Cedex, France (e-mail: [email protected])
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Abstract

We study a skew product with a curve of neutral points. We show that there exists a unique absolutely continuous invariant probability measure, and that the Birkhoff averages of a sufficiently smooth observable converge to a normal law or a stable law, depending on the average of the observable along the neutral curve.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 27 , Issue 1 , February 2007 , pp. 123 - 151
Copyright
2006 Cambridge University Press

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