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2013
Impact Factor

Adecarlos Carvalho

Av. dos Portugueses, 1966, Bacanga, Sao Luıs, MA, Brasil
Departamento de Matematica, Universidade Federal do Maranhao

Publications:

 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. Keywords: point vortex problem, relative equilibria, periodic orbits, Lyapunov center theorem Citation: Carvalho A., Cabral H. E.,  Lyapunov Orbits in the $n$-Vortex Problem on the Sphere, Regular and Chaotic Dynamics, 2015, vol. 20, no. 3, pp. 234-246 DOI:10.1134/S156035471503003X
 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. Keywords: point vortices, relative equilibria, periodic orbits, Lyapunov center theorem Citation: Carvalho A., Cabral H. E.,  Lyapunov Orbits in the $n$-Vortex Problem, Regular and Chaotic Dynamics, 2014, vol. 19, no. 3, pp. 348-362 DOI:10.1134/S156035471403006X