ANOSOV DIFFEOMORPHISM AND COUPLING
                             by
             Xavier Bressaud and Carlangelo Liverani

                            ABSTRACT

We prove the existence of an SRB measure and the exponential decay of
correlations for smooth 
observables for mixing Anosov $C^{1+\alpha}$ diffeormorphisms  
on a $d$-dimens\-ional ($d \geq 2$) Riemannian manifold. 
The novelty lies in the very simple method of proof.  
We construct explicitly  a coupling between two initial densities so
that under the 
action of the diffeomorphism, both components get closer and closer. The
speed of this 
convergence can be explicitly estimated and is directly related to 
the speed of decay of correlations. The existence of the SRB measure 
and its properties readily follow.