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

King Shun LEUNG; Jun Jason LUO

doi:10.1007/s10711-014-0033-9

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

King Shun LEUNG
, Jun Jason LUO

Department of Mathematics and Information Technology (MIT)

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

6 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 language	English
Pages (from-to)	145-157
Journal	Geometriae Dedicata
Volume	175
Issue number	1
Early online date	Nov 2014
DOIs	https://doi.org/10.1007/s10711-014-0033-9
Publication status	Published - Apr 2015

Keywords

Self-affine set
Digit set
ε-Connected
Connectedness

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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 {\textcopyright} 2014 Springer Science+Business Media Dordrecht.",

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AB - 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.

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

Abstract

Keywords

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