POINT VORTICES ON THE SPHERE: STABILITY OF SYMMETRIC RELATIVE EQUILIBRIA

被引：20

作者：

Laurent-Polz, Frederic ^{[1
]}

Montaldi, James ^{[2
]}

Roberts, Mark ^{[3
]}

机构：

[1] Inst Non Lineaire Nice, F-06560 Valbonne, France

[2] Univ Manchester, Sch Math, Manchester M13 9PL, Lancs, England

[3] Univ Surrey, Dept Math, Guildford GU2 7XH, Surrey, England

来源：

JOURNAL OF GEOMETRIC MECHANICS | 2011年 / 3卷 / 04期

关键词：

Point vortices; Hamiltonian systems; stability; bifurcations; symmetry; HAMILTONIAN-SYSTEMS; NONLINEAR STABILITY; VORTEX DYNAMICS; BIFURCATIONS; BODY;

D O I：

10.3934/jgm.2011.3.439

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We describe the linear and nonlinear stability and instability of certain symmetric configurations of point vortices on the sphere forming relative equilibria. These configurations consist of one or two rings, and a ring with one or two polar vortices. Such configurations have dihedral symmetry, and the symmetry is used to block diagonalize the relevant matrices, to distinguish the subspaces on which their eigenvalues need to be calculated, and also to describe the bifurcations that occur as eigenvalues pass through zero.

引用

页码：439 / 486

页数：48

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