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Connectedness of planar self-affine sets associated with non-consecutive collinear digit sets
- Publication Year :
- 2012
-
Abstract
- In the paper, we focus on the connectedness of planar self-affine sets $T(A,{\mathcal{D}})$ generated by an integer expanding matrix $A$ with $|\det (A)|=3$ and a collinear digit set ${\mathcal{D}}=\{0,1,b\}v$, where $b>1$ and $v\in {\mathbb{R}}^2$ such that $\{v, Av\}$ is linearly independent. We discuss the domain of the digit $b$ to determine the connectedness of $T(A,{\mathcal{D}})$. 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.<br />15 pages, 10 figures
- Subjects :
- Discrete mathematics
Social connectedness
Applied Mathematics
General Topology (math.GN)
Geometric Topology (math.GT)
Characterization (mathematics)
Connectedness
Set (abstract data type)
Combinatorics
Self-affine set
Neighbor
Matrix (mathematics)
Mathematics - Geometric Topology
Domain (ring theory)
FOS: Mathematics
Affine transformation
Linear independence
Collinear digit set
Analysis
Mathematics
Integer (computer science)
Mathematics - General Topology
Subjects
Details
- Language :
- English
- Database :
- OpenAIRE
- Accession number :
- edsair.doi.dedup.....239ee867ba0dc81f76f7fa1f7bb9c877