Nombre de rotation presque sûr des endomorphismes du cercle affines par morceaux

We define the almost sure rotation number for some degree one endomorphisms over the circle. It is the rotation number for almost any point of the circle. We describe it for a particular family of expanding piecewise affine endomorphisms. We show that its dependance on the parameters is H?lder for any exposant 0 < α < 1 but in general not Lipschitz. In particular the set of parameters which give an irrational almost sure rotation number has a Hausdorff dimension equal to 1. Received: 16 July 2001