Year: 2008
Type: preprint
Abstract: We consider $N$ point vortices $s_j$ of strengths $κ_j$ moving on a closed (compact, boundaryless, orientable) surface $S$ with riemannian metric $g$. As far as we know, only the sphere or surfaces of revolution, the latter qualitatively, have been treated in the available literature. The aim of this note is to present an intrinsic geometric formulation for the general case. We give a simple proof of Kimura's conjecture that a dipole describes geodesic motion. Searching for integrable vortex pairs systems on Liouville surfaces is in order. The vortex pair system on a triaxial ellipsoid extends Jacobi's geodesics. Is it Arnold-Liouville integrable? Not in our wildest dreams is another possibility: that quantizing a vortex system could relate with a million dollars worth question, but we took courage - nerve is more like it - to also present it.
Source: arXiv (Cornell University)
Authors: Boatto, Stefanella, Koiller, Jair
Language: English
Subfield: Astronomy and Astrophysics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4394643222