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Conformal measure and decay of correlation for covering weighted systems

Published online by Cambridge University Press:  01 December 1998

CARLANGELO LIVERANI ,
BENOIT SAUSSOL  and
SANDRO VAIENTI
CARLANGELO LIVERANI
Affiliation:
University of Rome, Tor Vergata, Rome, Italy
BENOIT SAUSSOL
Affiliation:
Centre de Physique Théorique, Luminy, Marseilles and PhyMat, Université de Toulon, France
SANDRO VAIENTI
Affiliation:
Centre de Physique Théorique, Luminy, Marseilles and PhyMat, Université de Toulon, France
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Abstract

We show that for a large class of piecewise monotonic transformations on a totally ordered, compact set one can construct conformal measures and obtain the exponential mixing rate for the associated equilibrium state. The method is based on the study of the Perron–Frobenius operator. The conformal measure, the density of the invariant measure and the rate of mixing are deduced by using an appropriate Hilbert metric, without any compactness arguments, even in the case of a countable to one transformation.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 18 , Issue 6 , December 1998 , pp. 1399 - 1420
Copyright
1998 Cambridge University Press

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