We prove a form of Arnold diffusion in the a-priori stable case. Let be a nearly integrable system of arbitrary degrees of freedom with a strictly convex H0. We show that for a “generic” , there exists an orbit satisfying where is independent of . The diffusion orbit travels along a codimension-1 resonance, and the only obstruction to our construction is a finite set of additional resonances.
For the proof we use a combination of geometric and variational methods, and manage to adapt tools which have recently been developed in the a-priori unstable case.
"Arnold diffusion in arbitrary degrees of freedom and normally hyperbolic invariant cylinders." Acta Math. 217 (1) 1 - 79, 2016. https://doi.org/10.1007/s11511-016-0141-5