@techreport{40f0b4eb8217477eac815d647db69861,
title = "Deformation of geometry and bifurcations of vortex rings",
abstract = "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.",
keywords = "vortices, curvature, symmetric bifurcations",
author = "James Montaldi and Tadashi Tokieda",
year = "2012",
month = apr,
language = "English",
isbn = "978-3034804509",
series = "MIMS Eprints",
publisher = "Manchester Institute for Mathematical Sciences School of Mathematics",
number = "2012.108",
type = "WorkingPaper",
institution = "Manchester Institute for Mathematical Sciences School of Mathematics",
}