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

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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。

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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.

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Methods and applications of analysis MATHEMATICS, APPLIED-

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33.30%

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