Is it possible for hamiltonian (dynamical) systems to have asymptotically stable rest points? By Liouville's theorem I got that for symplectic hamiltonian systems only Lyapunov stability is allowed.
My knowledge about symplectic manifolds is however limited and my question would be if it is possible for "non symplectic" hamiltonian (dynamical) systems to exist and to have asymptotically stable rest points.