{"title":"微分方程定性理论与二次有理函数动力学","authors":"Koh Katagata","doi":"10.12988/NADE.2014.3819","DOIUrl":null,"url":null,"abstract":"We study the qualitative theory of first order di fferential equations consisting of the iteration of complex quadratic rational functions and we focus on the configuration, namely location and stability, of simple equilibrium points which correspond to periodic points of the quadratic rational functions. Our main tools are properties of Julia sets of the quadratic rational functions and the Euler-Jacobi formula.","PeriodicalId":315586,"journal":{"name":"Nonlinear Analysis and Differential Equations","volume":"283 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"title\":\"Qualitative Theory of Differential Equations and Dynamics of Quadratic Rational Functions\",\"authors\":\"Koh Katagata\",\"doi\":\"10.12988/NADE.2014.3819\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We study the qualitative theory of first order di fferential equations consisting of the iteration of complex quadratic rational functions and we focus on the configuration, namely location and stability, of simple equilibrium points which correspond to periodic points of the quadratic rational functions. Our main tools are properties of Julia sets of the quadratic rational functions and the Euler-Jacobi formula.\",\"PeriodicalId\":315586,\"journal\":{\"name\":\"Nonlinear Analysis and Differential Equations\",\"volume\":\"283 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"1900-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Nonlinear Analysis and Differential Equations\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.12988/NADE.2014.3819\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Nonlinear Analysis and Differential Equations","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.12988/NADE.2014.3819","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Qualitative Theory of Differential Equations and Dynamics of Quadratic Rational Functions
We study the qualitative theory of first order di fferential equations consisting of the iteration of complex quadratic rational functions and we focus on the configuration, namely location and stability, of simple equilibrium points which correspond to periodic points of the quadratic rational functions. Our main tools are properties of Julia sets of the quadratic rational functions and the Euler-Jacobi formula.
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