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

King Shun LEUNG, Jun Jason LUO

Research output: Contribution to journalArticle

3 Citations (Scopus)

Abstract

We study a class of planar self-affine sets T (A, D) generated by the integer expanding matrices A with | det A| = 3 and the non-collinear digit sets D = {0, v, k Av} where k ∈ Z {0} and v ∈ R² such that {v, Av} is linearly independent. By examining the characteristic polynomials of A carefully, we prove that T (A, D) is connected if and only if the parameter k = ±1. Copyright © 2014 Springer Science+Business Media Dordrecht.
Original languageEnglish
Pages (from-to)145-157
JournalGeometriae Dedicata
Volume175
Issue number1
Early online dateNov 2014
DOIs
Publication statusPublished - Apr 2015

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Citation

Leung, S.-S., & Luo, J. J. (2015). Connectedness of planar self-affine sets associated with non-collinear digit sets. Geometriae Dedicata, 175(1), 145-157.

Keywords

  • Self-affine set
  • Digit set
  • ε-Connected
  • Connectedness