Projective metrics and mixing properties on towers

Maume-Deschamps, Véronique

doi:10.1090/S0002-9947-01-02786-6

Projective metrics and mixing properties on towers
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Trans. Amer. Math. Soc. 353 (2001), 3371-3389 Request permission

Abstract:

We study the decay of correlations for towers. Using Birkhoff’s projective metrics, we obtain a rate of mixing of the form: \[ c_n (f,g) \leq \operatorname {Ct} \alpha (n) \Vert f \Vert \, \Vert g \Vert _1\] 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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