On the Boundary of Self-Affine Sets

Qi-Rong Deng; Xiang-Yang Wang

doi:10.1155/2015/573604

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Home > Journals > Abstr. Appl. Anal. > Volume 2015 > Article

2015 On the Boundary of Self-Affine Sets

Qi-Rong Deng, Xiang-Yang Wang

Abstr. Appl. Anal. 2015: 1-3 (2015). DOI: 10.1155/2015/573604

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Abstract

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.