Mathematical Sciences: Faculty Publications
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
Copyright
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