Choreographic Holomorphic Spheres with Application to Hamiltonian Systems of $N$-Vortex Type

Abstract

We study the existence of (relative) simple choreographies for a class of Hamiltonian systems describing the interaction of particles in the plane motivated mainly by the n-vortex type problem. In particular, by constructing choreographic pseudo-holomorphic spheres, we prove that there exist infinitely many non-trivial relative choreographies for the identical n-vortex problem arising from both the Euler equation and the Gross-Pitaevskii equation.

arXiv comment31 pages, 4 figures

References in corpus (6)

• Absolute and relative choreographies in the problem of point vortices moving on a plane
• On the shape of vortices for a rotating Bose Einstein condensate
• Unchained polygons and the N-body problem
• Periodic solutions of the N-vortex Hamiltonian system in planar domains
• Choreographies in the $n$-vortex problem
• Global continua of periodic solutions of singular first-order Hamiltonian systems of N-vortex type