Instability of resonant invariant tori in Hamiltonian systems

TL;DR

This paper investigates the stability of resonant invariant tori in Hamiltonian systems, demonstrating various instability results when the tori have resonant frequencies, thus advancing understanding of their dynamical behavior.

Contribution

It provides new instability results for resonant invariant tori in Hamiltonian systems, highlighting conditions under which these tori are unstable.

Findings

Instability results for resonant invariant tori

Analysis of stability notions near quasi-periodic tori

Conditions leading to instability in Hamiltonian dynamics

Abstract

In this article, we consider the dynamics in a neighborhood of a quasi-periodic torus which is invariant by a Hamiltonian flow, we discuss several notions of stability and we prove several results of instability when the frequency of the invariant torus is resonant.