Some instability properties of resonant invariant tori in Hamiltonian systems

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.

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Received 4 January 2015

Accepted 31 August 2015

Published 7 June 2017