EXPONENTIAL RATE OF CORRELATION DECAY FOR CHARACTERS IN A 3-PARAMETERCLASS OF TORAL SKEW ENDOMORPHISMS

A detailed analysis of the correlation decay for characters in a three -parameter class of mappings of the 2-torus onto itself is presented. Being these mappings the natural extension of toral transformations pr eviously considered with regard to a model of modulated diffusion, the y show the structure of a skew product between the Bernoulli endomorph ism B-p(x) = pxmod[0, 1[, p is an element of Z\ {-1, 0, 1}, on the 1-t orus T-1:= [0, 1[ and a translation on T-1. The family of characters f or which correlation decay occurs is fully characterized for any choic e of the parameters, and the decay is proved to be exponential, with a rate analytically computable. This improves a previous result by W. P arry, provides a lower bound to the spectral radius of a Perron-Froben ius operator introduced by the same author in his proof and answers po sitively to the conjecture that the poorest is the rational approximat ion of the coupling parameter of the map the fastest is the decay rate .