Quasi-periodic solutions and stability of the equilibrium for quasi-periodically forced planar reversible and Hamiltonian systems under the Bruno condition

In this paper we investigate the existence of quasi-periodic solutions of non-autonomous two-dimensional reversible and Hamiltonian systems under the Bruno condition. As an application we study the dynamical stability of the trivial solution at the origin of a quasi-periodically forced planar system. Under a mild non-degeneracy condition we give a criterion that is necessary and sufficient for a large class of systems.