Relative Periodic Solutions Of The N-Vortex Problem Via The Variational Method

Abstract

This article studies the N-vortex problem in the plane with positive vorticities. After an investigation of some properties for normalised relative equilibria of the system, we use symplectic capacity theory to show that, there exist infinitely many normalised relative periodic orbits on a dense subset of all energy levels, which are neither fixed points nor relative equilibria.

arXiv comment22 pages, 4 figures

References in corpus (6)

• Vortex dynamics on a cylinder
• Unchained polygons and the N-body problem
• Periodic solutions of the N-vortex Hamiltonian system in planar domains
• Global continua of periodic solutions of singular first-order Hamiltonian systems of N-vortex type
• Relative periodic orbits in point vortex systems
• Morse Theory and Relative Equilibria in the Planar $n$-Vortex Problem

Cited by in corpus (2)

• Burst of Point Vortices and Non-Uniqueness of 2D Euler Equations
• Stability of periodic solutions of the N-vortex problem in general domains