#### Title

Dimensions of the Boundary of a Graph-Directed Self-Similar Set With Overlaps

#### Document Type

Article

#### Publication Date

2016

#### Publication Title

Houston Journal of Mathematics

#### Abstract

We set up a framework for computing the Hausdorff and box dimensions of the boundary of each component 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 the boundary of each component 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 boundary of a self-similar tile.

#### Recommended Citation

Deng, Guotai, Chuntai Liu, Sze-Man Ngai.
2016.
"Dimensions of the Boundary of a Graph-Directed Self-Similar Set With Overlaps."
*Houston Journal of Mathematics*, 42 (1): 179-210.

https://digitalcommons.georgiasouthern.edu/math-sci-facpubs/402