A well known Moser stability theorem states that a generic elliptic fixed point of an area-preserving mapping is Lyapunov stable. We investigate the question of Lyapunov stability for 4-dimensional resonant totally elliptic fixed points of symplectic maps. We show that gcnerically a convex, resonant, totally elliptic point of a symplectic map is Lyapunov unstable. The proof heavily relies on a proof of J. Mather of existence of Arnold diffusion for convex Hamiltonians in 2.5 degrees of freedom. The latter proof is announced in [Ma5], but still unpublished.
|Number of pages||38|
|Publication status||Published - 1 Dec 2004|