Negative Pell Equation and Stationary Configurations of Point Vortices on the Plane

被引：1

作者：

Vishnevskaya, A. D. ^{[1
]}

Demina, M. V. ^{[1
]}

机构：

[1] Moscow Inst Elect & Math, Higher Sch Econ, Moscow 123458, Russia

来源：

MATHEMATICAL NOTES | 2023年 / 114卷 / 1-2期

基金：

俄罗斯科学基金会;

关键词：

point vortex; infinite-dimensional configuration; stationary configuration; negative Pell equation; POLYNOMIALS; EQUILIBRIA; SYSTEMS;

D O I：

10.1134/S0001434623070040

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

The paper deals with the study of the model of point vortices proposed by the German scientist Hermann Helmholtz. Necessary and sufficient conditions for the existence of infinitely many nonequivalent stationary configurations are found for a system consisting of two point vortices of intensity Gamma(1) and an arbitrary number of point vortices of intensity Gamma(2). A classification of such configurations is carried out. For the first time, a connection is discovered between the negative Diophantine Pell equation and stationary configurations of point vortices on the plane.

引用

页码：46 / 54

页数：9

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