This article is cited in 6 papers

Lyapunov Orbits in the $n$-Vortex Problem

Adecarlos C. Carvalho^a, Hildeberto E. Cabral<sup>b

a</sup> Departamento de Matemática, Universidade Federal do Maranhão, Av. dos Portugueses, 1966, Bacanga, São Luís, MA, Brasil
^b Departamento de Matemática, Universidade Federal de Pernambuco, PVNS — UFS, Av. Ver. Olímpio Grande, s/n, Itabaiana, SE, Brasil

Abstract: 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 $\kappa$ is added to the ring of the polygonal configuration.

Keywords: point vortices; relative equilibria; periodic orbits; Lyapunov center theorem.

MSC: 76B47

Received: 01.10.2012
Accepted: 02.02.2014

Language: English

DOI: 10.1134/S156035471403006X

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