Lyapunov orbits in the n-vortex problem |
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Authors: | Adecarlos C Carvalho Hildeberto E Cabral |
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Institution: | 1. Departamento de Matemática, Universidade Federal do Maranh?o, Av. dos Portugueses, 1966, Bacanga, S?o Luís, MA, Brasil 2. Departamento de Matemática, Universidade Federal de Pernambuco, PVNS — UFS, Av. Ver. Olímpio Grande, s/n, Itabaiana, SE, Brasil
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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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