平面线性系统庞卡罗半映射的性质及其在分段系统周期轨道上的直接应用

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2021-09-26 DOI:10.14232/ejqtde.2023.1.22

V. Carmona, Fernando Fernández-Sánchez, E. García-Medina, D. Novaes

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引用次数: 2

摘要

本文讨论了平面线性系统在直线上定义的Poincaré半映射的基本性质。具体地，我们关注庞加莱半映射的分析性，它们在切点和无穷远处的级数展开式（Taylor和Newton–Puiseux），庞加莱半映射图与第四象限平分线之间的相对位置，以及它们的二阶导数的符号。所有这些性质对于理解平面分段线性系统的动力学行为至关重要。因此，我们还提供了关于周期轨道的一些最直接但不平凡的结果。

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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Properties of Poincaré half-maps for planar linear systems and some direct applications to periodic orbits of piecewise systems

This paper deals with fundamental properties of Poincaré half-maps defined on a straight line for planar linear systems. Concretely, we focus on the analyticity of the Poincaré half-maps, their series expansions (Taylor and Newton–Puiseux) at the tangency point and at infinity, the relative position between the graph of Poincaré half-maps and the bisector of the fourth quadrant, and the sign of their second derivatives. All these properties are essential to understand the dynamic behavior of planar piecewise linear systems. Accordingly, we also provide some of their most immediate, but non-trivial, consequences regarding periodic orbits.

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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.