We construct a smooth family of Hamiltonian systems, together with a family of group symmetries and momentum maps, for the dynamics of point vortices on surfaces, parametrized by the curvature of the surface. Equivariant bifurcations in this family are characterized, whence the stability of the Thomson heptagon is deduced without recourse to the Birkhoff normal form, which has hitherto been a necessary tool.
|Place of Publication||University of Manchester|
|Number of pages||26|
|Publication status||Published - Apr 2012|
|Publisher||Manchester Institute for Mathematical Sciences School of Mathematics|
- vortices, curvature, symmetric bifurcations