Gevrey genericity of Arnold diffusion in a priori unstable Hamiltonian systems

TL;DR

This paper proves that Arnold diffusion persists in a priori unstable Hamiltonian systems under generic Gevrey smooth perturbations, extending known results from $C^r$ smooth to Gevrey smooth cases using variational methods.

Contribution

It demonstrates the existence of Arnold diffusion in a priori unstable Hamiltonian systems with Gevrey smooth perturbations, a significant extension of previous $C^r$ smooth results.

Findings

Arnold diffusion exists under generic Gevrey smooth perturbations.

The proof employs variational methods.

Results apply to systems with two and a half degrees of freedom.

Abstract

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.