By using variational method and under generic condition, we show that Arnold diffusion exists in a priori hyperbolic and timeperiodic Hamiltonian systems with multiple degrees of freedom.
"Arnold diffusion in Hamiltonian systems: a priori unstable case." J. Differential Geom. 82 (2) 229 - 277, June 2009. https://doi.org/10.4310/jdg/1246888485