Liverani C., Saussol B., Vaienti S.
Conformal Measure and Decay of Correlation for Covering Weighted Systems.
(60K, LaTeX)
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 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.