Assouad type dimensions for self-affine sponges with a weak coordinate ordering condition

被引：2

作者：

Howroyd, Douglas C. ^{[1
]}

机构：

[1] Univ St Andrews, Sch Math & Stat, St Andrews KY16 9SS, Fife, Scotland

来源：

JOURNAL OF FRACTAL GEOMETRY | 2019年 / 6卷 / 01期

基金：

英国工程与自然科学研究理事会;

关键词：

Assouad dimension; lower dimension; self-affine set; weak tangent; HAUSDORFF DIMENSION; SETS;

D O I：

10.4171/JFG/69

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Recently self-affine sponges have been shown to be interesting counter-examples to several previously open problems. One class of recently studied sponges are Bedford-McMullen sponges with a weak coordinate ordering condition, that is, sponges with several coordinates having the same contraction ratio. The Assouad type dimensions of such sets cannot be calculated using the same formula as the regular Bedford-McMullen sponges. We calculate the Assouad type dimensions for such sponges and the more general Lalley-Gatzouras sponges with a weak coordinate ordering condition, discussing some of their more subtle details along the way.

引用

页码：67 / 88

页数：22