Mathematical Research Letters

Volume 24 (2017)

Number 1

Some instability properties of resonant invariant tori in Hamiltonian systems

Pages: 21 – 35



Abed Bounemoura (Université Paris Dauphine, CEREMADE, Paris, France)


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.

Received 4 January 2015

Accepted 31 August 2015

Published 7 June 2017