Gevrey genericity of Arnold diffusion in a priori unstable Hamiltonian systems

Qinbo Chen, Chong-Qing Cheng

Published 2017-10-22Version 1

It is well known that under generic $C^r$ perturbations, Arnold diffusion exists in the a priori unstable Hamiltonian systems. In this paper, by using variational method, we prove that under generic Gevrey-smooth perturbations, Arnold diffusion still exists in the a priori unstable Hamiltonian systems with two and a half degrees of freedom.