We study the existence of subharmonic solutions and solutions with complicated dynamics in a Duffing-type equation which arises from the study of forced tides. This is a model which involves an almost enclosed basin, connected to the sea by a narrow strait. Such a basin turns out to be a nonlinear Helmholtz resonator. The proofs are based on developments of the theory of topological horseshoes in connection with some geometric features associated to linked twist maps.
