Improved exponential stability for near-integrable quasi-convex Hamiltonians

TL;DR

This paper enhances the understanding of exponential stability in near-integrable quasi-convex Hamiltonian systems, offering sharper bounds on Arnold diffusion speed, which advances the theoretical framework of Hamiltonian dynamics.

Contribution

It provides improved exponential stability estimates for analytic and Gevrey perturbations, refining the upper bounds on Arnold diffusion speed in quasi-convex Hamiltonian systems.

Findings

Sharper upper bounds on Arnold diffusion speed

Enhanced exponential stability estimates

Optimality of the new bounds

Abstract

In this article, we improve previous results on exponential stability for analytic and Gevrey perturbations of quasi-convex integrable Hamiltonian systems. In particular, this provides a sharper upper bound on the speed of Arnold diffusion which we believe to be optimal.