Digit sets for connected tiles via similar matrices I: Dilation matrices with rational eigenvalues

Details Digit sets for connected tiles via similar matrices I: Dilation matrices with rational eigenvalues Digit sets for connected tiles via similar matrices I: Dilation matrices with rational eigenvalues

2010-03-31

arxiv.org/abs/1004.0004v1

Mathematics

General Topology

12 pages, 6 figures

Scientific paper

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).

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