Graph-Directed Iterated Function Systems with Overlaps

Manav Das; Sze Man Ngai

Graph-Directed Iterated Function Systems with Overlaps

Manav Das, Sze Man Ngai

Mathematical Sciences

Research output: Contribution to journal › Article › peer-review

20 Scopus citations

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.

Original language	American English
Journal	Indiana University Mathematics Journal
Volume	53
State	Published - Jan 1 2004

Keywords

Graph-directed
Iterated Function System
Overlaps

DC Disciplines

Education
Mathematics

Access to Document

http://www.jstor.org/stable/24903460

Cite this

@article{3976ac2ceab04a90bb4dca05e978686c,

title = "Graph-Directed Iterated Function Systems with Overlaps",

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.",

keywords = "Graph-directed, Iterated Function System, Overlaps",

author = "Manav Das and Ngai, {Sze Man}",

year = "2004",

month = jan,

day = "1",

language = "American English",

volume = "53",

journal = "Indiana University Mathematics Journal",

issn = "0022-2518",

publisher = "Indiana University",

}

TY - JOUR

T1 - Graph-Directed Iterated Function Systems with Overlaps

AU - Das, Manav

AU - Ngai, Sze Man

PY - 2004/1/1

Y1 - 2004/1/1

N2 - 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.

AB - 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.

KW - Graph-directed

KW - Iterated Function System

KW - Overlaps

UR - https://digitalcommons.georgiasouthern.edu/math-sci-facpubs/601

UR - http://www.jstor.org/stable/24903460

M3 - Article

SN - 0022-2518

VL - 53

JO - Indiana University Mathematics Journal

JF - Indiana University Mathematics Journal

ER -

Graph-Directed Iterated Function Systems with Overlaps

Abstract

Keywords

DC Disciplines

Access to Document

Other files and links

Fingerprint

Cite this