{"title":"New solutions of the Poincaré Center Problem in degree 3","authors":"Hans-Christian von Bothmer","doi":"arxiv-2409.01751","DOIUrl":null,"url":null,"abstract":"Let $\\omega$ be a plane autonomous system and C its configuration of\nalgebraic integral curves. If the singularities of C are quasi homogeneous we\ngive new conditions for existence of a Darboux integrating factor or a Darboux\nfirst integral. This is used to construct new components of the center variety\nin degree 3.","PeriodicalId":501035,"journal":{"name":"arXiv - MATH - Dynamical Systems","volume":"8 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-09-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - MATH - Dynamical Systems","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2409.01751","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
Abstract
Let $\omega$ be a plane autonomous system and C its configuration of
algebraic integral curves. If the singularities of C are quasi homogeneous we
give new conditions for existence of a Darboux integrating factor or a Darboux
first integral. This is used to construct new components of the center variety
in degree 3.
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