Digit sets for connected tiles via similar matrices I: Dilation matrices with rational eigenvalues
General Topology
2010-04-02 v1
Abstract
Given any m-dimensional dilation matrix A with rational eigenvalues, we demonstrate the existence of a digit set D such that the attractor T(A,D) of the iterated function system generated by A and D is connected. We give an easily verified sufficient condition on A for a specific digit set, which we call the centered canonical digit set for A, to give rise to a connected attractor T(A,D).
Keywords
Cite
@article{arxiv.1004.0004,
title = {Digit sets for connected tiles via similar matrices I: Dilation matrices with rational eigenvalues},
author = {Avra S. Laarakker and Eva Curry},
journal= {arXiv preprint arXiv:1004.0004},
year = {2010}
}
Comments
12 pages, 6 figures