Аннотация:
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, 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 $n$ vortices. We include numerical results for all cases, for various values of $n$, and we provide key details on the computational approach.
Образец цитирования:
Renato C. Calleja, Eusebius J. Doedel, Carlos García-Azpeitia, “Choreographies in the n-vortex Problem”, Regul. Chaotic Dyn., 23:5 (2018), 595–612
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\by Renato C. Calleja, Eusebius J. Doedel, Carlos Garc{\'\i}a-Azpeitia
\paper Choreographies in the n-vortex Problem
\jour Regul. Chaotic Dyn.
\yr 2018
\vol 23
\issue 5
\pages 595--612
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\crossref{https://doi.org/10.1134/S156035471805009X}
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Образцы ссылок на эту страницу:
https://www.mathnet.ru/rus/rcd348
https://www.mathnet.ru/rus/rcd/v23/i5/p595
Эта публикация цитируется в следующих 10 статьяx:
K. Constantineau, C. García-Azpeitia, L. C. García-Naranjo, J.-P. Lessard, “Determination of Stable Branches of Relative Equilibria of the N-Vortex Problem on the Sphere”, Commun. Math. Phys., 406:2 (2025)
Е. М. Артемова, “Динамика двух вихрей на конечном плоском цилиндре”, Вестн. Удмуртск. ун-та. Матем. Мех. Компьют. науки, 33:4 (2023), 642–658
Carlos García-Azpeitia, Luis C. García-Naranjo, “Platonic Solids and Symmetric Solutions of the N-vortex Problem on the Sphere”, J Nonlinear Sci, 32:3 (2022)
J. D'Ambroise, R. Carretero-González, P. Schmelcher, P. G. Kevrekidis, “Superfluid vortex multipoles and soliton stripes on a torus”, Phys. Rev. A, 105:6 (2022)
C. Garcia, “Vortex patches choreography for active scalar equations”, J. Nonlinear Sci., 31:5 (2021), 75
B. Bonnard, O. Cots, B. Wembe, “A Zermelo navigation problem with a vortex singularity”, ESAIM-Control OPtim. Calc. Var., 27:S (2021), S10
R. Calleja, C. Garcia-Azpeitia, J.-Ph. Lessard, J. D. M. James, “Torus knot choreographies in the n-body problem”, Nonlinearity, 34:1 (2021)
Carlos Balsa, Olivier Cots, Joseph Gergaud, Boris Wembe, Lecture Notes in Electrical Engineering, 695, CONTROLO 2020, 2021, 232
M. A. Sokolovskiy, K. V. Koshel, D. G. Dritschel, J. N. Reinaud, “N-symmetric Interaction of N Hetons. I. Analysis of the Case N=2”, Phys. Fluids, 32:9 (2020), 096601
C. Garcia-Azpeitia, “Relative periodic solutions of the n-vortex problem on the sphere”, J. Geom. Mech., 11:3 (2019), 427–438
Цитирование в формате AMSBIB
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