Nekhoroshev theorem for perturbations of the central motion

TL;DR

This paper proves a Nekhoroshev-type theorem for perturbed Hamiltonian systems describing a particle in a central potential, showing long-term stability of certain actions under explicit conditions.

Contribution

It establishes quasi-convexity of the Hamiltonian for central motion under specific potential conditions, enabling long-term stability results for perturbations.

Findings

Actions are approximately conserved for exponentially long times.

The Hamiltonian is shown to be quasi-convex under explicit potential conditions.

Provides a rigorous stability estimate for perturbed central motion.

Abstract

In this paper we prove a Nekhoroshev type theorem for perturbations of Hamiltonians describing a particle subject to the force due to a central potential. Precisely, we prove that under an explicit condition on the potential, the Hamiltonian of the central motion is quasi-convex. Thus, when it is perturbed, two actions (the modulus of the total angular momentum and the action of the reduced radial system) are approximately conserved for times which are exponentially long with the inverse of the perturbation parameter.