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2012.108: Deformation of geometry and bifurcations of vortex rings

2012.108: James Montaldi and Tadshi Tokieda (2013) Deformation of geometry and bifurcations of vortex rings. Springer Proceedings in Mathematics & Statistics, 35. pp. 335-370. ISSN 2194-1009

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DOI: 10.1007/978-3-0348-0451-6_14

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.

Item Type:Article
Uncontrolled Keywords:Point vortices, symmetric bifurcations, Hamiltonian systems, Family of symmetries
Subjects:MSC 2000 > 37 Dynamical systems and ergodic theory
MIMS number:2012.108
Deposited By:Dr James Montaldi
Deposited On:19 October 2013

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