Arnold's instability conjecture for generic elliptic equilibria

Let $H$ be an analytic Hamiltonian system with an elliptic equilibrium point, having $n$ degrees of freedom. Assume that $n\geq 3$ and that the quadratic part of the Hamiltonian at the equilibrium is not sign-definite. Arnold's conjecture. An elliptic equilibrium point of a generic analytic Hamiltonian system is Lyapounov unstable. The conjecture is wide open: under the standing real-analytic and non-resonance assumptions, no example is known, although examples exist in resonant or smooth non-analytic settings.