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• W2896883450 abstract "We consider the equations of motion of $n$ vortices of equal circulation in the plane, in a disk and on a sphere. The vortices form a polygonal equilibrium in a rotating frame of reference. We use numerical continuation in a boundary value setting to determine the Lyapunov families of periodic orbits that arise from the polygonal relative equilibrium. When the frequency of a Lyapunov orbit and the frequency of the rotating frame have a rational relationship then the orbit is also periodic in the inertial frame. A dense set of Lyapunov orbits, with frequencies satisfying a diophantine equation, corresponds to choreographies of the $n$ vortices. We include numerical results for all cases, for various values of $n$, and we provide key details on the computational approach." @default.
• W2896883450 created "2018-10-26" @default.
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• W2896883450 date "2018-09-01" @default.
• W2896883450 modified "2023-10-02" @default.
• W2896883450 title "Choreographies in the n-vortex Problem" @default.
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• W2896883450 doi "https://doi.org/10.1134/s156035471805009x" @default.
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