Mathematics > Dynamical Systems
[Submitted on 23 Apr 2018]
Title:Relative Periodic Solutions Of The N-Vortex Problem Via The Variational Method
View PDFAbstract: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.
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