On the Boundary of Self-Affine Sets
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 com...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Wiley
2015-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2015/573604 |
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| _version_ | 1832560488351793152 |
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| author | Qi-Rong Deng Xiang-Yang Wang |
| author_facet | Qi-Rong Deng Xiang-Yang Wang |
| author_sort | Qi-Rong Deng |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-ba500e0979224765b78b6ae2eeca06ce |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2015-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-ba500e0979224765b78b6ae2eeca06ce2025-02-03T01:27:28ZengWileyAbstract and Applied Analysis1085-33751687-04092015-01-01201510.1155/2015/573604573604On the Boundary of Self-Affine SetsQi-Rong Deng0Xiang-Yang Wang1Department of Mathematics, Fujian Normal University, Fuzhou 350117, ChinaSchool of Mathematics and Computational Science, Sun Yat-Sen University, Guangzhou 510275, ChinaThis 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.http://dx.doi.org/10.1155/2015/573604 |
| spellingShingle | Qi-Rong Deng Xiang-Yang Wang On the Boundary of Self-Affine Sets Abstract and Applied Analysis |
| title | On the Boundary of Self-Affine Sets |
| title_full | On the Boundary of Self-Affine Sets |
| title_fullStr | On the Boundary of Self-Affine Sets |
| title_full_unstemmed | On the Boundary of Self-Affine Sets |
| title_short | On the Boundary of Self-Affine Sets |
| title_sort | on the boundary of self affine sets |
| url | http://dx.doi.org/10.1155/2015/573604 |
| work_keys_str_mv | AT qirongdeng ontheboundaryofselfaffinesets AT xiangyangwang ontheboundaryofselfaffinesets |