Zakeri切片I的核心部件建模

IF 0.6 4区数学 Q3 MATHEMATICS

Moscow Mathematical Journal Pub Date : 2021-02-15 DOI:10.17323/1609-4514-2022-22-2-265-294

A. Blokh, L. Oversteegen, Anastasia Shepelevtseva, V. Timorin

{"title":"Zakeri切片I的核心部件建模","authors":"A. Blokh, L. Oversteegen, Anastasia Shepelevtseva, V. Timorin","doi":"10.17323/1609-4514-2022-22-2-265-294","DOIUrl":null,"url":null,"abstract":". The paper deals with cubic 1-variable polynomials whose Julia sets are connected. Fixing a bounded type rotation number, we obtain a slice of such polynomials with the origin being a ﬁxed Siegel point of the speciﬁed rotation number. Such slices as parameter spaces were studied by S. Zakeri, so we call them Zakeri slices . We give a model of the central part of a slice (the subset of the slice that can be approximated by hyperbolic polynomials with Jordan curve Julia sets), and a continuous projection from the central part to the model. The projection is deﬁned dynamically and agrees with the dynamical-analytic parameterization of the Principal Hyperbolic Domain by Petersen and Tan Lei.","PeriodicalId":54736,"journal":{"name":"Moscow Mathematical Journal","volume":"1 1","pages":""},"PeriodicalIF":0.6000,"publicationDate":"2021-02-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"title\":\"Modeling Core Parts of Zakeri Slices I\",\"authors\":\"A. Blokh, L. Oversteegen, Anastasia Shepelevtseva, V. Timorin\",\"doi\":\"10.17323/1609-4514-2022-22-2-265-294\",\"DOIUrl\":null,\"url\":null,\"abstract\":\". The paper deals with cubic 1-variable polynomials whose Julia sets are connected. Fixing a bounded type rotation number, we obtain a slice of such polynomials with the origin being a ﬁxed Siegel point of the speciﬁed rotation number. Such slices as parameter spaces were studied by S. Zakeri, so we call them Zakeri slices . We give a model of the central part of a slice (the subset of the slice that can be approximated by hyperbolic polynomials with Jordan curve Julia sets), and a continuous projection from the central part to the model. The projection is deﬁned dynamically and agrees with the dynamical-analytic parameterization of the Principal Hyperbolic Domain by Petersen and Tan Lei.\",\"PeriodicalId\":54736,\"journal\":{\"name\":\"Moscow Mathematical Journal\",\"volume\":\"1 1\",\"pages\":\"\"},\"PeriodicalIF\":0.6000,\"publicationDate\":\"2021-02-15\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Moscow Mathematical Journal\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.17323/1609-4514-2022-22-2-265-294\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Moscow Mathematical Journal","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.17323/1609-4514-2022-22-2-265-294","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}

引用次数: 1

摘要

本文讨论了Julia集是连通的三次一元多项式。固定一个有界型旋转数，我们得到了这样一个多项式的切片，其原点是指定旋转数的固定Siegel点。这种作为参数空间的切片是S.Zakeri研究的，所以我们称之为Zakeri切片。我们给出了切片的中心部分的模型（切片的子集，可以用Jordan曲线Julia集的双曲多项式来近似），以及从中心部分到模型的连续投影。该投影是动态定义的，与Petersen和Tan Lei对主双曲域的动力学分析参数化一致。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

Modeling Core Parts of Zakeri Slices I

. The paper deals with cubic 1-variable polynomials whose Julia sets are connected. Fixing a bounded type rotation number, we obtain a slice of such polynomials with the origin being a ﬁxed Siegel point of the speciﬁed rotation number. Such slices as parameter spaces were studied by S. Zakeri, so we call them Zakeri slices . We give a model of the central part of a slice (the subset of the slice that can be approximated by hyperbolic polynomials with Jordan curve Julia sets), and a continuous projection from the central part to the model. The projection is deﬁned dynamically and agrees with the dynamical-analytic parameterization of the Principal Hyperbolic Domain by Petersen and Tan Lei.

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

来源期刊

Moscow Mathematical Journal 数学-数学

CiteScore

1.40

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： The Moscow Mathematical Journal (MMJ) is an international quarterly published (paper and electronic) by the Independent University of Moscow and the department of mathematics of the Higher School of Economics, and distributed by the American Mathematical Society. MMJ presents highest quality research and research-expository papers in mathematics from all over the world. Its purpose is to bring together different branches of our science and to achieve the broadest possible outlook on mathematics, characteristic of the Moscow mathematical school in general and of the Independent University of Moscow in particular. An important specific trait of the journal is that it especially encourages research-expository papers, which must contain new important results and include detailed introductions, placing the achievements in the context of other studies and explaining the motivation behind the research. The aim is to make the articles — at least the formulation of the main results and their significance — understandable to a wide mathematical audience rather than to a narrow class of specialists.