This article is cited in 1 paper

Lyapunov Orbits in the $n$-Vortex Problem on the Sphere

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. Olímpio Grande, s/n Itabaiana, SE, Brasil

Abstract: In the phase space reduced by rotation, we prove the existence of periodic orbits of the $(n + 1)$-vortex problem emanating from a relative equilibrium formed by $n$ unit vortices at the vertices of a regular polygon at a fixed latitude and an additional vortex of intensity $\kappa$ at the north pole when the ideal fluid moves on the surface of a sphere.

Keywords: point vortex problem, relative equilibria, periodic orbits, Lyapunov center theorem.

MSC: 76B47, 37C27

Received: 17.03.2015

Language: English

DOI: 10.1134/S156035471503003X

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