A Hamiltonian approach for point vortices on non-orientable surfaces II: the Klein bottle

2022/02/13 by Nataliya A. Balabanova, Balabanova, Nataliya A.
Physics and Astronomy · #Dynamical Systems (math.DS) #FOS: Mathematics #Micro and Nano Robotics

paper · pdf · doi:10.48550/arxiv.2202.06175

openalex publication_date 2022/02/13 · openalex created_date 2022/04/03 · openalex updated_date 2026/07/28

Abstract

This is the second of two companion papers dedicated to the investigation of vortex motion on non-orientable surfaces. The first paper of the pair is predominantly concerned with establishing the Hamiltonian approach to systems of point vortices on non-orientable manifolds and investigating the limits of the intrinsic (restricted to the non-orientable manifold) approach. In addition, point vortex motion on the Mobius band is closely examined. In this paper, we investigate dynamics of one and two point vortices on the Klein bottle through establishing explicit forms of the Hamiltonian, equations of motion on the charts, describing relative equilibria, etc.

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