  The motion of a pair of counter-rotating point vortices placed in a uniform
flow around a circular cylinder forms a rich nonlinear system that is often
used to model vortex shedding. The phase portrait of the Hamiltonian governing
the dynamics of a vortex pair that moves symmetrically with respect to the
centerline---a case that can be realized experimentally by placing a splitter
plate in the center plane---is presented. The analysis provides new insights
and reveals novel dynamical features of the system, such as a nilpotent saddle
point at infinity whose homoclinic orbits define the region of nonlinear
stability of the so-called F\"oppl equilibrium. It is pointed out that a vortex
pair properly placed downstream can overcome the cylinder and move off to
infinity upstream. In addition, the nonlinear dynamics resulting from
antisymmetric perturbations of the F\"oppl equilibrium is studied and its
relevance to vortex shedding discussed.
