Relative periodic orbits in point vortex systems
Dynamical Systems
2009-11-10 v1 Mathematical Physics
math.MP
Abstract
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.
Cite
@article{arxiv.math/0401022,
title = {Relative periodic orbits in point vortex systems},
author = {Frederic Laurent-Polz},
journal= {arXiv preprint arXiv:math/0401022},
year = {2009}
}
Comments
27 pages, 17 figures