Adecarlos Carvalho
Av. dos Portugueses, 1966, Bacanga, Sao Luıs, MA, Brasil
Departamento de Matematica, Universidade Federal do Maranhao
Publications:
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Carvalho A., Cabral H. E.
Lyapunov Orbits in the $n$-Vortex Problem on the Sphere
2015, vol. 20, no. 3, pp. 234-246
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 κ at the north pole when the ideal fluid moves on the surface of a sphere.
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Carvalho A., Cabral H. E.
Lyapunov Orbits in the $n$-Vortex Problem
2014, vol. 19, no. 3, pp. 348-362
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 κ is added to the ring of the polygonal configuration.
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