Relative periodic solutions of the n-vortex problem on the sphere

2018/05/26 by Carlos García-Azpeitia, García-Azpeitia, Carlos
Engineering · Mathematics · #Spacecraft Dynamics and Control #Advanced Differential Equations and Dynamical Systems #Geometric Analysis and Curvature Flows

paper · pdf · doi:10.48550/arxiv.1805.10417

Abstract

This paper gives an analysis of the movement of n vortices on the sphere. When the vortices have equal circulation, there is a polygonal solution that rotates uniformly around its center. The main result concerns the global existence of relative periodic solutions that emerge from this polygonal relative equilibrium. In addition, it is proved that the families of relative periodic solutions contain dense sets of choreographies.

Related

• 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
• Determination of stable branches of relative equilibria of the N-vortex problem on the sphere
• Morse index and stability of the planar N-vortex problem
• On polygonal relative equilibria in the N-vortex problem