Instability of resonant invariant tori in Hamiltonian systems

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.

References in corpus (3)

• Normal forms, stability and splitting of invariant manifolds I. Gevrey Hamiltonians
• Normal forms, stability and splitting of invariant manifolds II. Finitely differentiable Hamiltonians
• Double exponential stability for generic real-analytic elliptic equilibrium points