Quartic Rigid Systems in the Plane and in the Poincaré Sphere

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2024-06-28 DOI:10.1007/s12346-024-01083-z

M. J. Álvarez, J. L. Bravo, L. A. Calderón

引用次数: 0

Abstract

We consider the planar family of rigid systems of the form \(x'=-y+xP(x,y), y'=x+yP(x,y)\), where P is any polynomial with monomials of degree one and three. This is the simplest non-trivial family of rigid systems with no rotatory parameters. The family can be compactified to the Poincaré sphere such that the vector field along the equator is not identically null . We study the centers, singular points and limit cycles of that family on the plane and on the sphere.

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平面和泊恩卡球面上的四元刚性系统

我们考虑形式为（x'=-y+xP(x,y), y'=x+yP(x,y)\）的刚性系统平面族，其中 P 是一阶和三阶单项式的任意多项式。这是最简单的无旋转参数的非三维刚体系统族。这个系可以紧凑到波恩卡莱球面上，这样沿赤道的矢量场就不是等效空的了。我们研究了该族在平面和球面上的中心、奇异点和极限循环。

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

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

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