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This article is cited in 6 scientific papers (total in 6 papers)
Lyapunov Orbits in the $n$-Vortex Problem
Adecarlos C. Carvalhoa, Hildeberto E. Cabralb a 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.
Received: 01.10.2012 Accepted: 02.02.2014
Citation:
Adecarlos C. Carvalho, Hildeberto E. Cabral, “Lyapunov Orbits in the $n$-Vortex Problem”, Regul. Chaotic Dyn., 19:3 (2014), 348–362
Linking options:
https://www.mathnet.ru/eng/rcd158 https://www.mathnet.ru/eng/rcd/v19/i3/p348
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Abstract page: | 139 | References: | 34 |
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