The Extended 16th Hilbert Problem for Discontinuous Piecewise Systems Formed by Linear Centers and Linear Hamiltonian Saddles Separated by a Nonregular Line

IF 1.9 4区数学 Q2 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS

International Journal of Bifurcation and Chaos Pub Date : 2023-12-30 DOI:10.1142/s0218127423501961

Jaume Llibre, C. Valls

引用次数: 0

Abstract

We study discontinuous piecewise linear differential systems formed by linear centers and/or linear Hamiltonian saddles and separated by a nonregular straight line. There are two classes of limit cycles: the ones that intersect the separation line at two points and the ones that intersect the separation line in four points, named limit cycles of type [Formula: see text] and limit cycles of type [Formula: see text], respectively. We prove that the maximum numbers of limit cycles of types [Formula: see text] and [Formula: see text] are two and one, respectively. We show that all these upper bounds are reached providing explicit examples.

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由线性中心和线性哈密顿鞍构成的、被非规则线分隔的不连续片断系统的扩展第 16 希尔伯特问题

我们研究的是由线性中心和/或线性哈密顿鞍构成的、被非规则直线分隔的不连续片断线性微分系统。极限循环有两类：与分离线两点相交的极限循环和与分离线四点相交的极限循环，分别称为[公式：见正文]类型的极限循环和[公式：见正文]类型的极限循环。我们证明[公式：见正文]和[公式：见正文]类型的极限循环的最大数目分别是两个和一个。我们将提供明确的例子来证明所有这些上限都可以达到。

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

International Journal of Bifurcation and Chaos 数学-数学跨学科应用

CiteScore

4.10

自引率

13.60%

发文量

237

审稿时长

2-4 weeks

期刊介绍： The International Journal of Bifurcation and Chaos is widely regarded as a leading journal in the exciting fields of chaos theory and nonlinear science. Represented by an international editorial board comprising top researchers from a wide variety of disciplines, it is setting high standards in scientific and production quality. The journal has been reputedly acclaimed by the scientific community around the world, and has featured many important papers by leading researchers from various areas of applied sciences and engineering. The discipline of chaos theory has created a universal paradigm, a scientific parlance, and a mathematical tool for grappling with complex dynamical phenomena. In every field of applied sciences (astronomy, atmospheric sciences, biology, chemistry, economics, geophysics, life and medical sciences, physics, social sciences, ecology, etc.) and engineering (aerospace, chemical, electronic, civil, computer, information, mechanical, software, telecommunication, etc.), the local and global manifestations of chaos and bifurcation have burst forth in an unprecedented universality, linking scientists heretofore unfamiliar with one another''s fields, and offering an opportunity to reshape our grasp of reality.