Reduction of the planar 4-vortex system at zero momentum
| dc.creator | Patrick, G. W. | |
| dc.date | 1999-10-07 | |
| dc.date | 2000-03-24 | |
| dc.date.accessioned | 2026-07-07T04:32:59Z | |
| dc.date.available | 2026-07-07T04:32:59Z | |
| dc.description | The system of four point vortices in the plane has relative equilibria that behave as composite particles, in the case where three of the vortices have strength $-Γ/3$ and one of the vortices has strength $Γ$. These relative equilibria occur at nongeneric momenta. The reduction of this system, at those momenta, by continuous and then discrete symmetries, classifies the 4-vortex states which have been observed as products of collisions of two such composite particles. In this article I explicitly calculate these reductions, and show they are qualitatively identical one degree of freedom systems on a cylinder. The flows on these reduced systems all have one stable equilibrium and one unstable equilibrium, and all the orbits are periodic except for two homoclinic connections to the unstable equilibrium. | |
| dc.description | Minor typographical corrections and slightly revised introduction. 9 pages, 5 figures. To appear EQUIDIFF/99 proceedings | |
| dc.identifier | https://arxiv.org/abs/math-ph/9910012 | |
| dc.identifier | http://arxiv.org/abs/math-ph/9910012 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/58409 | |
| dc.subject | Mathematical Physics | |
| dc.subject | Dynamical Systems | |
| dc.subject | Symplectic Geometry | |
| dc.title | Reduction of the planar 4-vortex system at zero momentum | |
| dc.type | text |