On the Boundary of Self-Affine Sets

Qi-Rong Deng and Xiang-Yang Wang

Abstract and Applied Analysis, 2015, vol. 2015, 1-3

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.

Date: 2015
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlaaa:573604

DOI: 10.1155/2015/573604

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