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

Dynamical Systems