Bassam Fayad: On stability of elliptic equilibria and quasi-periodic motion in Hamiltonian systems

Abstract: Stability of quasi-periodic motion is one of the oldest problems of mathematical physics and it played a foundational role in dynamics. We explore this stability from three points of views of
topological stability (Lyapunov stability), statistical stability (KAM theory), and effective stability (finite time stability). We study various mechanisms of diffusion that give rise to several results of instability, among which the first examples of real analytic Hamiltonians with unstable elliptic fixed points, or
unstable invariant quasi-periodic tori, with convergent or divergent Birkhoff normal forms.