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On the Boundary of Self-Affine Sets
oleh: Qi-Rong Deng, Xiang-Yang Wang
Format: | Article |
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Diterbitkan: | Wiley 2015-01-01 |
Deskripsi
This paper is devoted to studying the boundary behavior of self-affine sets. We prove that the boundary of an integral self-affine set has Lebesgue measure zero. In addition, we consider the variety of the boundary of a self-affine set when some other contractive maps are added. We show that the complexity of the boundary of the new self-affine set may be the same, more complex, or simpler; any one of the three cases is possible.