On the Boundary of Self‐Affine Sets

Qi-Rong Deng and Xiang-Yang Wang

Abstract and Applied Analysis, 2015, vol. 2015, issue 1

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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https://doi.org/10.1155/2015/573604

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnlaaa:v:2015:y:2015:i:1:n:573604

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