无穷保角迭代函数系统的维谱

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY Accounts of Chemical Research Pub Date : 2019-10-22 DOI:10.4171/JFG/112

Tushar Das, David Simmons

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引用次数: 1

摘要

保形迭代函数系统(CIFS)的维谱是其各个子系统极限集的所有Hausdorff维的集合。这个简短的说明提供了两种结构——(i)一个紧凑的完美集，它不能作为CIFS的维度谱实现;(ii)一个相似的IFS，其维数谱为零Hausdorff维数，因此不是一致完美的——这解决了Chousionis、Leykekhman和Urba 'nski提出的问题，并继续引发关于IFS维数谱的拓扑和度量性质的新猜想和问题。

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On the dimension spectra of infinite conformal iterated function systems

The dimension spectrum of a conformal iterated function system (CIFS) is the set of all Hausdorff dimensions of its various subsystem limit sets. This brief note provides two constructions -- (i) a compact perfect set that cannot be realized as the dimension spectrum of a CIFS; and (ii) a similarity IFS whose dimension spectrum has zero Hausdorff dimension, and thus is not uniformly perfect -- which resolve questions posed by Chousionis, Leykekhman, and Urba\'nski, and go on provoke fresh conjectures and questions regarding the topological and metric properties of IFS dimension spectra.

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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.

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