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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, FranceUniversité 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

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

Information

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