Deformation of geometry and bifurcations of vortex rings

Montaldi, James and Tokieda, Tadshi (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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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 2010, the AMS's Mathematics Subject Classification > 37 Dynamical systems and ergodic theory
Depositing User: Dr James Montaldi
Date Deposited: 19 Oct 2013
Last Modified: 20 Oct 2017 14:13

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