Connectedness of planar self-affine sets associated with non-consecutive collinear digit sets

King Shun LEUNG, Jun Jason LUO

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10 Citations (Scopus)

Abstract

In the paper, we focus on the connectedness of planar self-affine sets T (A, D) generated by an integer expanding matrix A with | det(A)| = 3 and a collinear digit set D = {0, 1, b}v, where b > 1 and v ∈ R2 such that {v, Av} is linearly independent. We discuss the domain of the digit b to determine the connectedness of T (A, D). Especially, a complete characterization is obtained when we restrict b to be an integer. Some results on the general case of | det(A)| > 3 are obtained as well. Copyright © 2012 Elsevier Inc. All rights reserved.
Original languageEnglish
Pages (from-to)208-217
JournalJournal of Mathematical Analysis and Applications
Volume395
Issue number1
DOIs
Publication statusPublished - Nov 2012

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Self-affine
Collinear
Connectedness
Digit
Integer
Linearly

Citation

Leung, K.-S., & Luo, J. J. (2012). Connectedness of planar self-affine sets associated with non-consecutive collinear digit sets. Journal of Mathematical Analysis and Applications, 395(1), 208-217.

Keywords

  • Connectedness
  • Self-affine set
  • Collinear digit set
  • Neighbor