展开螺旋I

IF 0.6 Q4 MATHEMATICS, APPLIED

Methods and applications of analysis Pub Date : 2016-03-10 DOI:10.4310/maa.2018.v25.n3.a3

A. Fish, L. Paunescu

{"title":"展开螺旋I","authors":"A. Fish, L. Paunescu","doi":"10.4310/maa.2018.v25.n3.a3","DOIUrl":null,"url":null,"abstract":". Inspired by the previous works by Freedman and He [FH], and Katznelson, Subhashis Nag, and Sullivan [KNS], we study the spiraling behaviour around a singularity of bi-Lipschitz homeomorphisms in R 2 . In particular, we show that there is no bi-Lipschitz homeomorphism of R 2 that maps a spiral with a sub-exponential decay of winding radii to an unwound arc. This result is sharp as shows an example of a logarithmic spiral.","PeriodicalId":18467,"journal":{"name":"Methods and applications of analysis","volume":null,"pages":null},"PeriodicalIF":0.6000,"publicationDate":"2016-03-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"5","resultStr":"{\"title\":\"Unwinding spirals I\",\"authors\":\"A. Fish, L. Paunescu\",\"doi\":\"10.4310/maa.2018.v25.n3.a3\",\"DOIUrl\":null,\"url\":null,\"abstract\":\". Inspired by the previous works by Freedman and He [FH], and Katznelson, Subhashis Nag, and Sullivan [KNS], we study the spiraling behaviour around a singularity of bi-Lipschitz homeomorphisms in R 2 . In particular, we show that there is no bi-Lipschitz homeomorphism of R 2 that maps a spiral with a sub-exponential decay of winding radii to an unwound arc. This result is sharp as shows an example of a logarithmic spiral.\",\"PeriodicalId\":18467,\"journal\":{\"name\":\"Methods and applications of analysis\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.6000,\"publicationDate\":\"2016-03-10\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"5\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Methods and applications of analysis\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.4310/maa.2018.v25.n3.a3\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"MATHEMATICS, APPLIED\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Methods and applications of analysis","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.4310/maa.2018.v25.n3.a3","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}

引用次数: 5

摘要

．受Freedman和He [FH]以及Katznelson, Subhashis Nag, and Sullivan [KNS]先前工作的启发，我们研究了r2中双lipschitz同纯态在奇点周围的螺旋行为。特别地，我们证明了r2中不存在双lipschitz同纯映射，它将一个绕圈半径呈次指数衰减的螺旋映射为一个未绕圈的弧。作为对数螺旋的一个例子，这个结果是清晰的。

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

Unwinding spirals I

. Inspired by the previous works by Freedman and He [FH], and Katznelson, Subhashis Nag, and Sullivan [KNS], we study the spiraling behaviour around a singularity of bi-Lipschitz homeomorphisms in R 2 . In particular, we show that there is no bi-Lipschitz homeomorphism of R 2 that maps a spiral with a sub-exponential decay of winding radii to an unwound arc. This result is sharp as shows an example of a logarithmic spiral.

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

Methods and applications of analysis MATHEMATICS, APPLIED-

自引率

33.30%

发文量