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In the reduced phase space by rotation, we prove the existence of periodic orbits of the n-vortex problem emanating from a relative equilibrium formed by n unit vortices at the vertices of a regular polygon, both in the plane and at a fixed latitude when the ideal fluid moves on the surface of a sphere. In the case of a plane we also prove the existence of such periodic orbits in the (n + 1)-vortex problem, where an additional central vortex of intensity κ is added to the ring of the polygonal configuration.
Regular and Chaotic Dynamics – Springer Journals
Published: Jun 6, 2014
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