Semi-analytical estimates for the speed of diffusion in the second fundamental model of resonance: a Jeans-Landau-Teller approach

We consider the problem of slow chaotic diffusion in a near-integrable three-dimensional hamiltonian system, in the context of the second fundamental model of resonance. Performing analytical estimates for a class of Melnikov integrals, we provide an upper bound for the rate of diffusion. Analytical estimates are based on the so-called stationary phase approximation. We apply our analysis to a problem arising in celestial mechanics: the first order (3:2) asteroidal mean motion resonance in the restricted elliptic three-body problem.