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In this paper we study existence of Normally Hyperbolic Invariant Laminations(NHIL) for a nearly integrable system given by the product of the pendulum andthe rotator perturbed with a small coupling between the two. This example wasintroduced by Arnold. Using a {\it separatrix map}, introduced in a lowdimensional case by Zaslavskii-Filonenko and studied in a multidimensional caseby Treschev and Piftankin, for an open class of trigonometric perturbations weprove that NHIL do exist. Moreover, using a second order expansion for theseparatrix map from [GKZ], we prove that the system restricted to this NHIL isa skew product of nearly integrable cylinder maps. Application of the resultsfrom [CK] about random iteration of such skew products show that in the proper$\varepsilon$-dependent time scale the push forward of a Bernoulli measuresupported on this NHIL weakly converges to an Ito diffusion process on the lineas $\varepsilon$ tends to zero.

Normally Hyperbolic Invariant Laminations and diffusive behaviour for the generalized Arnold example away from resonances