Gevrey genericity of Arnold diffusion in a priori unstable Hamiltonian systems

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.

46 pages, 5 figures

References in corpus (5)

• Arnold diffusion in arbitrary degrees of freedom and normally hyperbolic invariant cylinders
• A second order expansion of the separatrix map for trigonometric perturbations of a priori unstable systems
• Destruction of invariant circles for Gevrey area-preserving twist maps
• Regular dependence of the Peierls barriers on perturbations
• Renormalization of Gevrey vector fields with a Brjuno type arithmetical condition

Cited by in corpus (1)

• Analytic genericity of diffusing orbits in a priori unstable Hamiltonian systems