指数映射的哈雷方法的非连通Julia集

Pub Date : 2022-03-06 DOI:10.1080/14689367.2022.2048633

P. Cumsille, J. González–Marín, Gerardo Honorato, Diego Lugo

{"title":"指数映射的哈雷方法的非连通Julia集","authors":"P. Cumsille, J. González–Marín, Gerardo Honorato, Diego Lugo","doi":"10.1080/14689367.2022.2048633","DOIUrl":null,"url":null,"abstract":"We investigate the Halley method of exponential maps. Our main result is that, unlike Newton's method, the Julia set of Halley's method may be disconnected when applied to entire maps of form where p and q are polynomials and q is non-constant. We also describe the nature of the fixed points and classify rational Halley's maps of entire functions.","PeriodicalId":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2022-03-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Disconnected Julia set of Halley's method for exponential maps\",\"authors\":\"P. Cumsille, J. González–Marín, Gerardo Honorato, Diego Lugo\",\"doi\":\"10.1080/14689367.2022.2048633\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We investigate the Halley method of exponential maps. Our main result is that, unlike Newton's method, the Julia set of Halley's method may be disconnected when applied to entire maps of form where p and q are polynomials and q is non-constant. We also describe the nature of the fixed points and classify rational Halley's maps of entire functions.\",\"PeriodicalId\":0,\"journal\":{\"name\":\"\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0,\"publicationDate\":\"2022-03-06\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1080/14689367.2022.2048633\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1080/14689367.2022.2048633","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}

引用次数: 0

摘要

我们研究了指数映射的哈雷方法。我们的主要结果是，与牛顿方法不同，哈雷方法的Julia集在应用于p和q为多项式且q为非常数的整个形式映射时可能是断开的。我们还描述了不动点的性质，并对整个函数的有理哈雷映射进行了分类。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文

微信好友朋友圈 QQ好友复制链接

Disconnected Julia set of Halley's method for exponential maps

We investigate the Halley method of exponential maps. Our main result is that, unlike Newton's method, the Julia set of Halley's method may be disconnected when applied to entire maps of form where p and q are polynomials and q is non-constant. We also describe the nature of the fixed points and classify rational Halley's maps of entire functions.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助