The Integrability and Linearizability of Cubic $$Z_2$$ -Equivariant Systems with Two 1: $$-q$$ Resonant Saddle Points

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2024-08-22 DOI:10.1007/s12346-024-01128-3

Xiongkun Wang, Changjian Liu

引用次数: 0

Abstract

In this article, the integrability and linearizability of a class of cubic $Z_2$-equivariant systems $\dot{x}=-\frac{1}{2}x-a_{21}y+\frac{1}{2}x^3+a_{21}x^2y+a_{12}xy^2+a_{03} y^3,\, \dot{y}=(-q-b_{21})y+b_{21}x^2y+b_{12}xy^2+b_{03}y^3, $ are studied. For any positive integer q, we obtain the first three saddle quantities of the above systems by theoretical analysis. Moreover, for any positive integer q, we derive the necessary and sufficient conditions for the linearizability of the above systems under some assumptions.

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具有两个 1: $$-q$$ 共振鞍点的立方 $$Z_2$$ 参数系统的可积分性与线性化

本文研究了一类立方$Z_2$-可变系统 \(\dot{x}=-\frac{1}{2}x-a_{21}y+\frac{1}{2}x^3+a_{21}x^2y+a_{12}xy^2+a_{03} y^3 的可整性和线性化、\, \dot{y}=(-q-b_{21})y+b_{21}x^2y+b_{12}xy^2+b_{03}y^3, \）进行研究。对于任意正整数 q，我们通过理论分析得到了上述系统的前三个鞍量。此外，对于任意正整数 q，我们推导出了上述系统在某些假设条件下线性化的必要条件和充分条件。

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

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.