$\mathbb{C}^2$中的有趣例子是与恒等式相切的无吸引域的映射

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2016-04-05 DOI:10.4171/jfg/84

Sara Lapan

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引用次数: 0

摘要

我们在$\mathbb{C}^2$中给出一个有趣的映射的例子，它与恒等式相切，但在它的任何特征方向上都没有吸引域。这张地图有三个特征方向，其中两个不吸引，而第三个吸引指向那个方向，但不指向原点。此外，我们表明，如果我们在这个图中加入更高次的项，有时沿着它的一个特征方向存在一个吸引域，有时不存在。

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Interesting examples in $\mathbb{C}^2$ of maps tangent to the identity without domains of attraction

We give an interesting example of a map in $\mathbb{C}^2$ that is tangent to the identity, but that does not have a domain of attraction along any of its characteristic direction. This map has three characteristic directions, two of which are not attracting while the third attracts points to that direction, but not to the origin. In addition, we show that if we add higher degree terms to this map, sometimes a domain of attraction along one of its characteristic directions will exist and sometimes one will not.

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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.