Chirikov and Nekhoroshev diffusion estimates: bridging the two sides of the river

PABLO CINCOTTA; CHRISTOS EFTTYMIOPOULOS; CLAUDIA GIORDANO; MARTÍN MESTRE

Paraty

Workshop; 44th Annual Meeting of the Division on Dynamical Astronomy of the American Astronomical Society; 2013

American Astronomical Society

We present theoretical and numerical results pointing towards a strong connection between the estimates for the diffusion rate along simple resonances in multidimensional nonlinear Hamiltonian 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 estimatesis made for ten values of the perturbation parameter, showing a very satisfactory agreement.