完全可积分微分系统的局部稳定性和拓扑结构

IF 1.8 3区数学 Q1 MATHEMATICS, APPLIED Nonlinear Analysis-Real World Applications Pub Date : 2024-12-01 Epub Date: 2024-06-24 DOI:10.1016/j.nonrwa.2024.104172

Yantao Yang , Xiang Zhang , Zhiyu Wang

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引用次数: 0

摘要

完全可积分系统在常识上是动力学简单的，但在其第一积分不函数独立的点附近，它们可能具有复杂的动力学。Tudoran 在 2017 年提出了表征完全可积分系统非退化正则奇点稳定性的准则。在这里，我们提出了一个比 Tudoran 的标准更有用的新标准，即他的标准适用的情况也适用于我们的标准，而有些情况我们的标准适用，但他的标准不适用。

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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Local stability and topological structure of completely integrable differential systems

Completely integrable systems are dynamically simple in common sense, but they may have complicated dynamics around the points where their first integrals are not functionally independent. Tudoran in 2017 provided a criterion for characterizing stability of nondegenerated regular singularities of completely integrable systems. Here we present a new criterion which is more useful than that by Tudoran, in the sense that the cases that his criterion works on are also applicable to ours, whereas there are cases that our criterion works on but his does not.

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来源期刊

Nonlinear Analysis-Real World Applications 数学-应用数学

CiteScore

3.80

自引率

5.00%

发文量

176

审稿时长

59 days

期刊介绍： Nonlinear Analysis: Real World Applications welcomes all research articles of the highest quality with special emphasis on applying techniques of nonlinear analysis to model and to treat nonlinear phenomena with which nature confronts us. Coverage of applications includes any branch of science and technology such as solid and fluid mechanics, material science, mathematical biology and chemistry, control theory, and inverse problems. The aim of Nonlinear Analysis: Real World Applications is to publish articles which are predominantly devoted to employing methods and techniques from analysis, including partial differential equations, functional analysis, dynamical systems and evolution equations, calculus of variations, and bifurcations theory.