Diffusion phenomena in multidimensional systems: A possible bridge between two antagonist theories?

CINCOTTA, P.M.; EFTHYMIOPOULOS, C.; GIORDANO, C. M.; MESTRE, M.

Serra Negra - SP

Congreso; XVI Coloquio Brasileiro de Dinámica Orbital; 2012

IME

We present theoretical and numerical results pointing towards a strong connection between the estimates for the diffusion rate along simple resonances in multidimensional nonlinear Hamil- tonian systems that can be obtained using the heuristic theory of Chirikov and a more formal one due to Nekhoroshev. We show that, despite a wide-spread impression, the two theories are complementary rather than antagonist. In fact, we take advantage of this complementarity in order to obtain accurate theoretical predictions for the value of the diffusion coefficient along a resonance in a specific 3DoF nearly integrable Hamiltonian system. Besides, we compute numerically the diffusion coefficient and a full comparison of all estimates is made for ten values of the perturbation parameter, showing a very satisfactory agreement.