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Decay of correlations and mixing properties in a dynamical system with zero K–S entropy

Published online by Cambridge University Press:  17 April 2001

M. COURBAGE  and
D. HAMDAN
M. COURBAGE
Affiliation:
Laboratoire de Probabilités, 4, Place Jussieu, Tour 56, 3ème Etage 75252, Paris Cedex 05, France Université Paris VII, L.P.T.M., Tour Centrale, 2, Place Jussieu 75251, Paris Cedex 05, France
D. HAMDAN
Affiliation:
Laboratoire de Probabilités, 4, Place Jussieu, Tour 56, 3ème Etage 75252, Paris Cedex 05, France
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Abstract

We consider the ergodic skew product of translations on the torus ${\Bbb T}^{2}$. We characterize a class of smooth functions with exponential correlation decay rate and a class of subsets with an exponential rate of mixing. We show that the class of functions with sub-exponential correlation decay rate is generic. We also characterize another class of subsets with mixing rate of the order of $1/t$.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 17 , Issue 1 , February 1997 , pp. 87 - 103
Copyright
1997 Cambridge University Press

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