Deformation of geometry and bifurcation of vortex rings
Dynamical Systems
2012-10-23 v1
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
Cite
@article{arxiv.1210.5662,
title = {Deformation of geometry and bifurcation of vortex rings},
author = {James Montaldi and Tadashi Tokieda},
journal= {arXiv preprint arXiv:1210.5662},
year = {2012}
}
Comments
26 pages