Thomson's Heptagon: a case of bifurcation at infinity

S. Boatto^(1) and C. Sim\'o^(2)
(1) Depto de Matematica, U. Federal de Rio de Janeiro,
 Caixa postal 68530, Ilha do Fundao, Rio de Janeiro, RJ, CEP 21945-970, Brazil
(2) Dept. Matematica Aplicada i Analisi, U. Barcelona
 Gran Via 585, 08007 Barcelona, Spain

Abstract: Vortex modelling has a long history. Descartes (1944) used it as a
model for the solar system. J.J.Thomson (1883) used it as a model for the atom.
We consider point-vortex systems, which can be regarded as "discrete" solutions
of the Euler equation. Their dynamics is described by a Hamiltonian system of
equations. We are interested in polygonal configurations and how their stability
depends upon various dynamical variables. A bit of Celestial Mechanics'
techmiques helped us to simplify a problem that has been studied during over
a century.