{"title":"Local stability and topological structure of completely integrable differential systems","authors":"Yantao Yang , Xiang Zhang , Zhiyu Wang","doi":"10.1016/j.nonrwa.2024.104172","DOIUrl":null,"url":null,"abstract":"<div><p>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.</p></div>","PeriodicalId":49745,"journal":{"name":"Nonlinear Analysis-Real World Applications","volume":"80 ","pages":"Article 104172"},"PeriodicalIF":1.8000,"publicationDate":"2024-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Nonlinear Analysis-Real World Applications","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S1468121824001123","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"2024/6/24 0:00:00","PubModel":"Epub","JCR":"Q1","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
引用次数: 0
Abstract
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.
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.
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