Effective stability for slow time-dependent near-integrable Hamiltonians and application

TL;DR

This paper proves effective stability for slowly time-dependent near-integrable Hamiltonian systems and extends existing stability results to systems with arbitrary time-dependent potentials.

Contribution

It introduces a new stability theorem for non-autonomous Hamiltonians with slow time dependence and applies it to generalize prior stability results.

Findings

Effective stability holds for slow time-dependent perturbations.

Extended stability results to systems with arbitrary time-dependent potentials.

Provides a framework for analyzing stability in non-autonomous Hamiltonian systems.

Abstract

The aim of this note is to prove a result of effective stability for a non-autonomous perturbation of an integrable Hamiltonian system, provided that the perturbation depends slowly on time. Then we use this result to clarify and extend a stability result of Giorgilli and Zehnder for a mechanical system with an arbitrary time-dependent potential.