Relative periodic orbits in point vortex systems

Details Relative periodic orbits in point vortex systems Relative periodic orbits in point vortex systems

2004-01-05

arxiv.org/abs/math/0401022v1

Mathematics

Dynamical Systems

27 pages, 17 figures

Scientific paper

10.1088/0951-7715/17/6/001

We give a method to determine relative periodic orbits in point vortex systems: it consists mainly into perform a symplectic reduction on a fixed point submanifold in order to obtain a two-dimensional reduced phase space. The method is applied to point vortices systems on a sphere and on the plane, but works for other surfaces with isotropy (cylinder, ellipsoid, ...). The method permits also to determine some relative equilibria and heteroclinic cycles connecting these relative equilibria.

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