Connectedness of planar self-affine sets associated with non-consecutive collinear digit sets
Connectedness of planar self-affine sets associated with non-consecutive collinear digit sets
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DOI：
10.1016/j.jmaa.2012.05.034
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发表时间：
2012-05
影响因子：
1.3
通讯作者：
K. Leung;J. Luo
中科院分区：
文献类型：
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作者：
K. Leung;J. Luo
本文研究了由整数扩张矩阵A生成的平面自仿射集T(A，D)的连通性，其中b>；1和v∈R2使得{v，Av}是线性无关的。我们讨论了数字b的定义域，以确定T(A，D)的连通性。特别地，当我们将b限制为整数时，得到了一个完整的刻画。在|Det(A)|>；3的一般情况下也得到了一些结果。
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∈R2such 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.