{"title":"System without Characteristic Directions with a Nonanalytic Center Condition","authors":"","doi":"10.1134/s0012266123120030","DOIUrl":null,"url":null,"abstract":"<span> <h3>Abstract</h3> <p> A real autonomous differential system of the fifth degree with a degenerate singular point without characteristic directions is obtained. The necessary and sufficient condition for the center at a given point is determined by a function that is not analytic at the boundary point of the set of system parameters for which the singular point of the system is monodromic. An asymptotic representation of this function is calculated at the point where its analyticity is violated. </p> </span>","PeriodicalId":50580,"journal":{"name":"Differential Equations","volume":"25 1","pages":""},"PeriodicalIF":0.8000,"publicationDate":"2023-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Differential Equations","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1134/s0012266123120030","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
A real autonomous differential system of the fifth degree with a degenerate singular point without characteristic directions is obtained. The necessary and sufficient condition for the center at a given point is determined by a function that is not analytic at the boundary point of the set of system parameters for which the singular point of the system is monodromic. An asymptotic representation of this function is calculated at the point where its analyticity is violated.
期刊介绍：
Differential Equations is a journal devoted to differential equations and the associated integral equations. The journal publishes original articles by authors from all countries and accepts manuscripts in English and Russian. The topics of the journal cover ordinary differential equations, partial differential equations, spectral theory of differential operators, integral and integral–differential equations, difference equations and their applications in control theory, mathematical modeling, shell theory, informatics, and oscillation theory. The journal is published in collaboration with the Department of Mathematics and the Division of Nanotechnologies and Information Technologies of the Russian Academy of Sciences and the Institute of Mathematics of the National Academy of Sciences of Belarus.
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