We consider the motion of N vortex-points on a sphere,
with vortex-points fixed at both poles, which is a Hamiltonian
dynamical system. I will give a method for reducing
the system to an invariant low-dimensional dynamical system using
an invariance property with respect to certain transformations. The
reduction enables us to decompose the many
vortex-point problem into a collection of small systems of
vortex-points.
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