STATISTICAL PROPERTIES OF SKEW-ENDOMORPHISMS WITH BERNOULLI BASE

We analyse numerically the statistical properties of a class of mappin gs of the 2-torus T-2 onto itself, whose investigation is suggested by some models of modulated diffusion. These transformations can be writ ten as a skew-product of the endomorphism B-p(x) = px mod 1, p epsilon Z\{-1, 0, 1}, on the 1-torus T-1 := [0, 1[and a translation on T-1. U nder suitable assumptions the skew-product can be proven to be mixing w.r.t. the Lebesgue measure. Central Limit (CL) and Functional Central Limit (FCL) properties are numerically checked for analytic observabl es. The result is remarkable because the mappings show no hyperbolic o r quasi-hyperbolic structure, crucial for the proof of Central Limit T heorem and Donsker's Invariance Principle in all of the dynamical syst ems where these properties have been established up to now. Moreover, CL and FCL behaviours seem to hold also in the case of purely ergodic endomorphisms and even for observables whose correlations do not decay at infinity.