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:
Adecarlos C. Carvalho, Hildeberto E. Cabral, “Lyapunov Orbits in the n-Vortex Problem on the Sphere”, Regul. Chaotic Dyn., 20:3 (2015), 234–246
\Bibitem{CarCab15}
\by Adecarlos C. Carvalho, Hildeberto E. Cabral
\paper Lyapunov Orbits in the $n$-Vortex Problem on the Sphere
\jour Regul. Chaotic Dyn.
\yr 2015
\vol 20
\issue 3
\pages 234--246
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\crossref{https://doi.org/10.1134/S156035471503003X}
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Linking options:
https://www.mathnet.ru/eng/rcd31
https://www.mathnet.ru/eng/rcd/v20/i3/p234
This publication is cited in the following 1 articles:
Eugene A. Ryzhov, Konstantin V. Koshel, “Parametric Instability of a Many Point-vortex System in a Multi-layer Flow Under Linear Deformation”, Regul. Chaotic Dyn., 21:3 (2016), 254–266
Citation in format AMSBIB
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