期刊论文

Deng, Guotai

英文

HOUSTON JOURNAL OF MATHEMATICS

0362-1588

2016

42

1

179-210

The first author is supported by China Scholarship Council; the second author is supported by Hubei Provincial Department of Education scientific research plan project B2013221; the third author is supported in part by the National Natural Science Foundation of China grant 11271122. Part of this work was carried out while the first two authors were visiting the Department of Mathematical Sciences of Georgia Southern University. They are very grateful to the Department for its hospitality and support.

本校为其他机构

We set up a framework for computing the Hausdorff and box dimensions of the boundary of each component Fi of a graph self-similar family defined by a graph-directed iterated function system satisfying the so-called graph finite boundary type condition. We show that ∂Fi has the same Hausdorff and box dimension, with the corresponding Hausdorff measure being positive and σ-finite. These results are natural extensions of existing ones concerning the dimensions of the boun...