2012.108: Deformation of geometry and bifurcations of vortex rings
2012.108: James Montaldi and Tadshi Tokieda (2012) Deformation of geometry and bifurcations of vortex rings. In: Recent Trends in Dynamical Systems, 11-13 Jan 2012, Munich, Germany.
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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.
|Item Type:||Conference or Workshop Item (Paper)|
|Uncontrolled Keywords:||Point vortices, symmetric bifurcations, Hamiltonian systems, Family of symmetries|
|Subjects:||MSC 2000 > 37 Dynamical systems and ergodic theory|
|Deposited By:||Dr James Montaldi|
|Deposited On:||25 October 2012|