SOME APPLICATIONS OF SYMBOLIC DYNAMICS TECHNIQUES TO TORAL SKEW ENDOMORPHISMS

A class of dynamical systems of the 2-torus T-2 is considered. These s ystems have the farm of a skew product between the Bernoulli endomorph ism B-p(x) = px mod 1, p is an element of Z \ {-1, 0, 1}, defined on t he 1-torus T = [0, 1) and a translation on T itself. Symbolic dynamics techniques allow one to single out wide classes of observables which show an exponential decay of correlations. For some observables the ra te of correlation decay can be explicitly estimated.