Exponentially small splitting and Arnold diffusion for multiple time scale systems

We consider the class of Hamiltonians: 1/2 Sigma(j=1)(n-1) I-j(2) + 1/2epsilonI(n)(2) + p(2)/2 + epsilon[(cos q - 1) - b(2)(cos 2q - 1)] + epsilonmuf(q) Sigma(i-1)(n)sin(psi(i)), where 0 less than or equal to b less than or equal to 1/2, and the perturbing function f (q) is a rational function of e(4q). We 2 prove upper and lower bounds on the splitting for such class of systems, in regions of the phase space characterized by one fast frequency. Finally using an appropriate Normal Form theorem we prove the existence of chains of heteroclinic intersections.