Finiteness of mirror-symmetric relative equilibria of point vortices

IF 2.7 3区数学 Q1 MATHEMATICS, APPLIED

Physica D: Nonlinear Phenomena Pub Date : 2025-07-19 DOI:10.1016/j.physd.2025.134823

Kevin A. O’Neil

引用次数: 0

Abstract

Some relative equilibrium configurations of

n

point vortices in the plane have a mirror symmetry. In this paper it is proved that for arbitrary

n

and generic choice of vortex strengths, the mirror-symmetric configurations with no more than six vortices off the line of symmetry are finite in number. The same analysis is extended to include eight off-axis vortices when restricting to

n = 8

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点涡的镜像对称相对平衡的有限性

平面上n个点涡的一些相对平衡构型具有镜像对称性。本文证明了在任意n和一般涡旋强度选择下，不超过6个涡旋偏离对称线的镜像对称构型是有限的。当限制为n=8时，将相同的分析扩展为包括8个离轴涡。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Physica D: Nonlinear Phenomena 物理-物理：数学物理

CiteScore

7.30

自引率

7.50%

发文量

213

审稿时长

65 days

期刊介绍： Physica D (Nonlinear Phenomena) publishes research and review articles reporting on experimental and theoretical works, techniques and ideas that advance the understanding of nonlinear phenomena. Topics encompass wave motion in physical, chemical and biological systems; physical or biological phenomena governed by nonlinear field equations, including hydrodynamics and turbulence; pattern formation and cooperative phenomena; instability, bifurcations, chaos, and space-time disorder; integrable/Hamiltonian systems; asymptotic analysis and, more generally, mathematical methods for nonlinear systems.