{"title":"谐振微分系统线性化的爆破法","authors":"B. Ferčec, Maja Zulj, J. Giné","doi":"10.1142/s0218127423501006","DOIUrl":null,"url":null,"abstract":"In this paper, the linearizability of a [Formula: see text] resonant differential system is studied. First, we describe a method to compute the necessary conditions for linearizability based on blow-up transformation. Using the method, we compute necessary linearizability conditions for a family of [Formula: see text] resonant system with quadratic nonlinearities. The sufficiency of the obtained conditions is proven either by the Darboux linearization method or using the recursive procedure after blow-up transformation.","PeriodicalId":13688,"journal":{"name":"Int. J. Bifurc. Chaos","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2023-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Blow-Up Method for Linearizability of Resonant Differential Systems\",\"authors\":\"B. Ferčec, Maja Zulj, J. Giné\",\"doi\":\"10.1142/s0218127423501006\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this paper, the linearizability of a [Formula: see text] resonant differential system is studied. First, we describe a method to compute the necessary conditions for linearizability based on blow-up transformation. Using the method, we compute necessary linearizability conditions for a family of [Formula: see text] resonant system with quadratic nonlinearities. The sufficiency of the obtained conditions is proven either by the Darboux linearization method or using the recursive procedure after blow-up transformation.\",\"PeriodicalId\":13688,\"journal\":{\"name\":\"Int. J. Bifurc. Chaos\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2023-06-30\",\"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/s0218127423501006\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Int. J. Bifurc. Chaos","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1142/s0218127423501006","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Blow-Up Method for Linearizability of Resonant Differential Systems
In this paper, the linearizability of a [Formula: see text] resonant differential system is studied. First, we describe a method to compute the necessary conditions for linearizability based on blow-up transformation. Using the method, we compute necessary linearizability conditions for a family of [Formula: see text] resonant system with quadratic nonlinearities. The sufficiency of the obtained conditions is proven either by the Darboux linearization method or using the recursive procedure after blow-up transformation.
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