Graph-Directed Iterated Function Systems with Overlaps

Authors

Manav DasFollow
Sze-Man Ngai, Georgia Southern UniversityFollow

Document Type

Article

Publication Date

2004

Publication Title

Indiana University Mathematics Journal

ISSN

0022-2518

Abstract

We extend the finite type condition to graph-directed iterated function systems with overlaps. Under this condition, we describe algorithms to compute the box dimension and Hausdorff dimension of the corresponding graph self-similar sets and show that these dimensions agree; moreover, the Hausdorff measure of these sets is shown to be strictly positive.

Recommended Citation

Das, Manav, Sze-Man Ngai. 2004. "Graph-Directed Iterated Function Systems with Overlaps." Indiana University Mathematics Journal, 53 (1): 109-134. source: https://www.jstor.org/stable/24903460?seq=1#page_scan_tab_contents
https://digitalcommons.georgiasouthern.edu/math-sci-facpubs/601