{"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}
引用次数: 5
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.
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