平面和泊恩卡球面上的四元刚性系统

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

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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。

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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

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

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.

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