{"title":"Weak Centers and Local Bifurcation of Critical Periods in a Z2-Equivariant Vector Field of Degree 5","authors":"Yusen Wu, Feng Li","doi":"10.1142/s0218127423500293","DOIUrl":null,"url":null,"abstract":"With the help of algebraic manipulator-Mathematica, we identify the order of weak centers at [Formula: see text] and the origin as well as the number of local critical periods in a [Formula: see text]-equivariant vector field of degree 5. We show that [Formula: see text] and the origin can be weak centers of infinite order (i.e. isochronous center) and at most fourth-order weak centers of finite order. Furthermore, we prove that at most four local critical periods bifurcate from the bicenter and the origin, respectively. Our approach is a combination of computational algebraic techniques.","PeriodicalId":13688,"journal":{"name":"Int. J. Bifurc. Chaos","volume":"12 1","pages":"2350029:1-2350029:19"},"PeriodicalIF":0.0000,"publicationDate":"2023-03-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Int. J. Bifurc. Chaos","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1142/s0218127423500293","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
With the help of algebraic manipulator-Mathematica, we identify the order of weak centers at [Formula: see text] and the origin as well as the number of local critical periods in a [Formula: see text]-equivariant vector field of degree 5. We show that [Formula: see text] and the origin can be weak centers of infinite order (i.e. isochronous center) and at most fourth-order weak centers of finite order. Furthermore, we prove that at most four local critical periods bifurcate from the bicenter and the origin, respectively. Our approach is a combination of computational algebraic techniques.