2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/81042We offer a new method of reduction for a system of point vortices on a plane and a sphere. This method is similar to the classical node elimination procedure. However, as applied to the vortex dynamics, it requires substantial modification. Reduction of four vortices on a sphere is given in more detail. We also use the Poincare surface-of-section technique to perform the reduction a four-vortex system on a sphere.10 pages, 3 figuresExactly Solvable and Integrable Systemstext