Nonintegrability of two problems in vortex dynamics

An analysis is presented of two problems in vortex dynamics whose equations can be written in the Hamiltonian form. They are: the interaction of three coaxial vortex rings and the motion of four point vortices on a sphere. The nonintegrability of these problems in the restricted formulation is demonstrated analytically by the method of split separatrices, using a small parameter. (c) 1997 American Institute of Physics.