We prove the existence of an arbitrarily large number of subharmonic solutions for a class of weakly coupled Hamiltonian systems which includes the case when the Hamiltonian function is periodic in all of its variables and its critical points are non-degenerate. Our results are obtained through a careful analysis of the dynamics of the planar components, combined with an application of a generalized version of the Poincaré–Birkhoff Theorem.
