Gevrey Genericity Of Arnold Diffusion In A Priori Unstable Hamiltonian Systems

It is well known that under generic C(R) smooth perturbations, the phenomenon of global instability, known as Arnold diffusion, exists in a priori unstable Hamiltonian systems. In this paper, by using variational methods, we will prove that under generic Gevrey smooth perturbations, Arnold diffusion still exists in the a priori unstable Hamiltonian systems of two and a half degrees of freedom.