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, providing sharper bounds on Arnold diffusion speed, which advances the theoretical limits of stability in Hamiltonian dynamics.

Contribution

It offers improved exponential stability estimates for quasi-convex Hamiltonians with analytic and Gevrey perturbations, refining the upper bounds on Arnold diffusion speed.

Findings

Sharper exponential stability bounds

Optimal upper bounds on Arnold diffusion speed

Enhanced understanding of stability in Hamiltonian systems

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.