Аннотация:
This paper is concerned with the problem of three vortices on a sphere S2 and the Lobachevsky plane L2. After reduction, the problem reduces in both cases to investigating a Hamiltonian system with a degenerate quadratic Poisson bracket, which makes it possible to study it using the methods of Poisson geometry. This paper presents a topological classification of types of symplectic leaves depending on the values of Casimir functions and system parameters.
Ключевые слова:
Poisson geometry, point vortices, reduction, quadratic Poisson bracket, spaces of constant curvature, symplectic leaf, collinear configurations.
The work of A.V. Borisov (Sections 1 and 2) and I.A. Bizyaev (Section 4) was carried out within the framework of the state assignment to the Ministry of Education and Science of Russia (1.2404.2017/4.6). The work of I. S. Mamaev (Section 3) is carried out at MIPT under project 5-100 for state support for leading universities of the Russian Federation. Also this work is supported by the Russian Foundation for Basic Research (Project No. 17-01-00846-a).
Поступила в редакцию: 02.08.2018 Принята в печать: 04.09.2018
Образец цитирования:
Alexey V. Borisov, Ivan S. Mamaev, Ivan A. Bizyaev, “Three Vortices in Spaces of Constant Curvature: Reduction, Poisson Geometry, and Stability”, Regul. Chaotic Dyn., 23:5 (2018), 613–636
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\paper Three Vortices in Spaces of Constant Curvature: Reduction, Poisson Geometry, and Stability
\jour Regul. Chaotic Dyn.
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\issue 5
\pages 613--636
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Образцы ссылок на эту страницу:
https://www.mathnet.ru/rus/rcd349
https://www.mathnet.ru/rus/rcd/v23/i5/p613
Эта публикация цитируется в следующих 5 статьяx:
Е. М. Артемова, “Динамика двух вихрей на конечном плоском цилиндре”, Вестн. Удмуртск. ун-та. Матем. Мех. Компьют. науки, 33:4 (2023), 642–658
Elizaveta M. Artemova, Evgeny V. Vetchanin, “The Motion of an Unbalanced Circular Disk
in the Field of a Point Source”, Regul. Chaotic Dyn., 27:1 (2022), 24–42
Q. Wang, “The n-vortex problem on a Riemann sphere”, Commun. Math. Phys., 385:1 (2021), 565–593
E. M. Artemova, E. V. Vetchanin, “Control of the motion of a circular cylinder in an ideal fluid using a source”, Вестн. Удмуртск. ун-та. Матем. Мех. Компьют. науки, 30:4 (2020), 604–617
Björn Gebhard, Rafael Ortega, “Stability of Periodic Solutions of the N-vortex Problem in General Domains”, Regul. Chaotic Dyn., 24:6 (2019), 649–670
Цитирование в формате AMSBIB
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