Periodic motions of fluid particles induced by a prescribed vortex path in a circular domain

•A two-dimensional ideal fluid inside a circular domain under the action of a prescribed stirring protocol.•The motion of advected particles follows a Hamiltonian system.•The vortex induces a singularity on the angular variable.•An infinite number of periodic solutions are found.

By means of a generalized version of the Poincaré–Birkhoff theorem, we prove the existence and multiplicity of periodic solutions for a Hamiltonian system modeling the evolution of advected particles in a two-dimensional ideal fluid inside a circular domain and under the action of a point vortex with prescribed periodic trajectory.