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

2018/11/15 by Qun Wang, Wang, Qun
Mathematics · Physics and Astronomy · #37J05 #37N10 #70F10 #70H12 #Dynamical Systems (math.DS) #FOS: Mathematics #Geometric and Algebraic Topology #Nonlinear Waves and Solitons #Quantum chaos and dynamical systems #math.DS #msc:37J05 #msc:37N10 #msc:70F10 #msc:70H12

paper · pdf · doi:10.48550/arxiv.1811.06595

31 pages, 4 figures

arxiv created 2018/11/15 · openalex publication_date 2018/11/15 · arxiv updated 2018/11/19 · openalex created_date 2018/11/29 · openalex updated_date 2026/07/28

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.

Related

• Relative periodic solutions of the n-vortex problem on the sphere
• New periodic solutions for three or four identical vortices on a plane and a sphere
• Platonic solids and symmetric solutions of the N-vortex problem on the sphere
• Torus knot choreographies in the n-body problem
• Choreographies with Dihedral Symmetry in the Planar n-Body Problem