Smooth Siegel disks everywhere

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2019-11-22 DOI:10.24033/ast.1112

A. Avila, Xavier Buff, Arnaud Ch'eritat

引用次数: 1

Abstract

We prove the existence of Siegel disks with smooth boundaries in most families of holomorphic maps fixing the origin. The method can also yield other types of regularity conditions for the boundary. The family is required to have an indifferent fixed point at $0$, to be parameterized by the rotation number $\alpha$, to depend on $\alpha$ in a Lipschitz-continuous way, and to be non-degenerate. A degenerate family is one for which the set of non-linearizable maps is not dense. We give a characterization of degenerate families, which proves that they are quite exceptional.

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到处都是光滑的西格尔圆盘

证明了在大多数固定原点的全纯映射族中存在光滑边界的西格尔盘。该方法还可以得到其他类型的边界正则性条件。要求该族在$0$处有一个无关的不动点，由旋转数$\ α $参数化，以Lipschitz-continuous方式依赖于$\ α $，并且是非简并的。退化族是非线性映射集合不密集的族。我们给出了退化家庭的特征，证明它们是相当特殊的。

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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来源期刊

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.