Abstract
We derive a symplectic reduction of the evolution equations for a system of three interacting point vortices in the plane, first introducing Jacobi coordinates, then Lie-Poisson reductions, and finally reparameterizing the resulting leaves, arriving at an integrable system on a topologically nontrivial phase space surface. The reduced system is convenient for describing all aspects of three-vortex dynamics, including finite-time collapse, the calculation of relative equilibria and their stability, and scattering. We use the final simplified system to succinctly and geometrically explain a kind of bifurcation diagram that has appeared in the literature.
Atul Anurag (अतुल अनुराग)
Visiting Assistant Professor, Ramapo College of New Jersey
Roy Goodman
Professor, Associate Chair for Graduate Studies, Department of Mathematical Sciences
My research interests include dynamical systems and nonlinear waves, vortex dynamics, quantum graphs, and network inference