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Projective metrics and mixing properties on towers

Author(s): Véronique Maume-Deschamps
Journal: Trans. Amer. Math. Soc. 353 (2001), 3371-3389.
MSC (2000): Primary 37A25, 37C30, 37C40
Posted: April 9, 2001
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Abstract:

We study the decay of correlations for towers. Using Birkhoff's projective metrics, we obtain a rate of mixing of the form:

\begin{displaymath}c_n (f,g) \leq \text{\rm Ct} \alpha(n) \Vert f \Vert \, \Vert g \Vert_1\end{displaymath}

where $\alpha(n)$ goes to zero in a way related to the asymptotic mass of upper floors, $\Vert f\Vert$ is some Lipschitz norm and $\Vert g \Vert_1$ is some $L^1$ norm. The fact that the dependence on $g$ is given by an $L^1$ norm is useful to study asymptotic laws of successive entrance times.

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Additional Information:

Véronique Maume-Deschamps
Affiliation: Département de Mathématiques, Université de Genève, Geneva, Switzerland
Address at time of publication: Université de Bourgogne, B.P. 47870, 21078 Dijon Cedex, France
Email: vmaume@topolog.u-bourgogne.fr

DOI: 10.1090/S0002-9947-01-02786-6
PII: S 0002-9947(01)02786-6
Keywords: Decay of correlations, tower, transfer operator, projective metrics
Received by editor(s): May 23, 1999
Received by editor(s) in revised form: January 13, 2000
Posted: April 9, 2001
Copyright of article: Copyright 2001, American Mathematical Society

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