An explicit formula for the pressure of box-like affine iterated function systems

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2017-03-27 DOI:10.4171/JFG/72

I. Morris

引用次数: 6

Abstract

In this article we investigate the pressure function and affinity dimension for iterated function systems associated to the "box-like" self-affine fractals investigated by D.-J. Feng, Y. Wang and J.M. Fraser. Combining previous results of V. Yu. Protasov, A. K\"aenm\"aki and the author we obtain an explicit formula for the pressure function which makes it straightforward to compute the affinity dimension of box-like self-affine sets. We also prove a variant of this formula which allows the computation of a modified singular value pressure function defined by J.M. Fraser. We give some explicit examples where the Hausdorff and packing dimensions of a box-like self-affine fractal may be easily computed.

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盒状仿射迭代函数系统压力的显式公式

在本文中，我们研究了与D.-J.Feng、Y.Wang和J.M.Fraser研究的“盒状”自仿射分形相关的迭代函数系统的压力函数和亲和维数。结合余以前的研究结果。Protasov，A.K“aenm”aki和作者得到了压力函数的一个显式公式，使计算盒状自仿射集的亲和维数变得简单。我们还证明了这个公式的一个变体，它允许计算J.M.Fraser定义的修正奇异值压力函数。我们给出了一些明确的例子，其中盒状自仿射分形的Hausdorff维数和堆积维数可以很容易地计算。

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.