Three Vortices in Spaces of Constant Curvature: Reduction, Poisson Geometry, and Stability

被引：5

作者：

Borisov, Alexey V. ^{[1
]}

Mamaev, Ivan S. ^{[2
]}

Bizyaev, Ivan A. ^{[1
]}

机构：

[1] Udmurt State Univ, Ul Univ Skaya 1, Izhevsk 426034, Russia

[2] Moscow Inst Phys & Technol, Inst Per 9, Dolgoprudnyi 141700, Russia

来源：

REGULAR & CHAOTIC DYNAMICS | 2018年 / 23卷 / 05期

基金：

俄罗斯基础研究基金会;

关键词：

Poisson geometry; point vortices; reduction; quadratic Poisson bracket; spaces of constant curvature; symplectic leaf; collinear configurations; 2 POINT VORTICES; VORTEX SOURCES; DEFORMATION FLOW; DYNAMICS; MOTION; SPHERE; SURFACES; FLUID; PLANE; WAVE;

D O I：

10.1134/S1560354718050106

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This paper is concerned with the problem of three vortices on a sphere S-2 and the Lobachevsky plane L-2. 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.

引用

页码：613 / 636

页数：24

共 50 条

[1] Three Vortices in Spaces of Constant Curvature: Reduction, Poisson Geometry, and Stability
Alexey V. Borisov
Ivan S. Mamaev
Ivan A. Bizyaev
Regular and Chaotic Dynamics, 2018, 23 : 613 - 636
[2] Reduction and relative equilibria for the two-body problem on spaces of constant curvature
Borisov, A. V.
Garcia-Naranjo, L. C.
Mamaev, I. S.
Montaldi, J.
CELESTIAL MECHANICS & DYNAMICAL ASTRONOMY, 2018, 130 (06)
[3] A differential geometric approach to multiple view geometry in spaces of constant curvature
Ma, Y
INTERNATIONAL JOURNAL OF COMPUTER VISION, 2004, 58 (01) : 37 - 53
[4] A Differential Geometric Approach to Multiple View Geometry in Spaces of Constant Curvature
Yi Ma
International Journal of Computer Vision, 2004, 58 : 37 - 53
[5] Reduction and relative equilibria for the two-body problem on spaces of constant curvature
A. V. Borisov
L. C. García-Naranjo
I. S. Mamaev
J. Montaldi
Celestial Mechanics and Dynamical Astronomy, 2018, 130
[6] Graded geometry and Poisson reduction
Cattaneo, A. S.
Zambon, M.
SPECIAL METRICS AND SUPERSYMMETRY, 2009, 1093 : 48 - +
[7] Superintegrability on the Dunkl oscillator model in three-dimensional spaces of constant curvature
Dong, Shi-Hai
Najafizade, Amene
Panahi, Hossein
Chung, Won Sang
Hassanabadi, Hassan
ANNALS OF PHYSICS, 2022, 444
[8] Toward a Theory of Spaces of Constant Curvature
V. S. Dryuma
Theoretical and Mathematical Physics, 2006, 146 : 34 - 44
[9] SPECTRAL PROBLEMS IN SPACES OF CONSTANT CURVATURE
Benguria, Rafael D.
MATHEMATICAL RESULTS IN QUANTUM PHYSICS, 2011, : 131 - 137
[10] Rolling problems on spaces of constant curvature
Jurdjevic, Velimir
Zimmerman, Jason
LAGRANGIAN AND HAMILTONIAN METHODS FOR NONLINEAR CONTROL 2006, 2007, 366 : 221 - +

← 1 2 3 4 5 →