平面和泊恩卡球面上的四元刚性系统

IF 1.9 3区数学 Q1 MATHEMATICS

Qualitative Theory of Dynamical Systems Pub Date : 2024-06-28 DOI:10.1007/s12346-024-01083-z

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

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引用次数: 0

摘要

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。

Quartic Rigid Systems in the Plane and in the Poincaré Sphere

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Quartic Rigid Systems in the Plane and in the Poincaré Sphere

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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来源期刊

Qualitative Theory of Dynamical Systems MATHEMATICS, APPLIED-MATHEMATICS

CiteScore

2.50

自引率

14.30%

发文量

130

期刊介绍： Qualitative Theory of Dynamical Systems (QTDS) publishes high-quality peer-reviewed research articles on the theory and applications of discrete and continuous dynamical systems. The journal addresses mathematicians as well as engineers, physicists, and other scientists who use dynamical systems as valuable research tools. The journal is not interested in numerical results, except if these illustrate theoretical results previously proved.