{"title":"A uniform C1 connecting lemma for singular flows","authors":"Ming Li , Xingzhong Liu","doi":"10.1016/j.jde.2025.02.043","DOIUrl":null,"url":null,"abstract":"<div><div>We extend the uniform <span><math><msup><mrow><mi>C</mi></mrow><mrow><mn>1</mn></mrow></msup></math></span> connecting lemma <span><span>[28]</span></span> to singular flows. The perturbation parameters are valid in a <span><math><msup><mrow><mi>C</mi></mrow><mrow><mn>1</mn></mrow></msup></math></span>-neighborhood of the given vector field. Moreover, they are also uniform on the points except singularities and some periodic ones with small period.</div></div>","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":"429 ","pages":"Pages 247-261"},"PeriodicalIF":2.4000,"publicationDate":"2025-02-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Differential Equations","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0022039625001627","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
We extend the uniform connecting lemma [28] to singular flows. The perturbation parameters are valid in a -neighborhood of the given vector field. Moreover, they are also uniform on the points except singularities and some periodic ones with small period.
期刊介绍：
The Journal of Differential Equations is concerned with the theory and the application of differential equations. The articles published are addressed not only to mathematicians but also to those engineers, physicists, and other scientists for whom differential equations are valuable research tools.
Research Areas Include:
• Mathematical control theory
• Ordinary differential equations
• Partial differential equations
• Stochastic differential equations
• Topological dynamics
• Related topics
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