Lyapunov unstable elliptic equilibria

A new diffusion mechanism from the neighborhood of elliptic equilibria for Hamiltonian flows in three or more degrees freedom is introduced. We thus obtain explicit real entire Hamiltonians on R 2 d \mathbb {R}^{2d} , alttext="d greater-than-or-equal-to 4"> ? 4 encoding="application/x-tex">d\geq 4 that have a Lyapunov unstable equilibrium with an arbitrary chosen frequency vector whose coordinates are not all same sign. For non-resonant vectors, our examples divergent Birkhoff normal form at equilibrium. On {R}^4 we give having and form.