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

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