The box dimension of self-affine graphs and repellers

被引：46

作者：

Bedford, Tim ^{[1
]}

机构：

[1] Delft Univ Technol, Fac Math & Informat, NL-2600 AJ Delft, Netherlands

来源：

NONLINEARITY | 1989年 / 2卷 / 01期

关键词：

D O I：

10.1088/0951-7715/2/1/005

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The box dimension (or 'capacity') of a class of self-affine sets in the plane is calculated. The formula for box dimension given here has a similar form to Bowen's formula for the Hausdorff dimension of self-similar sets, involving the topological pressure of certain functions. The sets studied here appear in two contexts; as graphs of generalised Weientrass functions and as repellen in some foliation presewing maps of the cylinder. We use the techniques of the 'singularity spectrum' in order to carry out the calculations.

引用

页码：53 / 71

页数：19

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