New periodic solutions for three or four identical vortices on a plane and a sphere

2005/07/26 by А. В. Борисов, A. V. Borisov, Borisov, A. V. +6
Earth and Planetary Sciences · Physics and Astronomy · #Astro and Planetary Science #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Physical sciences #Geophysics and Gravity Measurements #Solar and Space Plasma Dynamics #nlin.SI

paper · pdf · doi:10.48550/arxiv.nlin/0507058

15 pages, 6 figures

arxiv created 2005/07/26 · openalex publication_date 2005/07/26 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper we describe new classes of periodic solutions for point vortices on a plane and a sphere. They correspond to similar solutions (so-called choreographies) in celestial mechanics.

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