| 摘要: |
| 本文研究了一类多分支自相似集的自仿嵌入.利用压缩映射的不动点,在一定条件下,证明了若一个自相似集能自仿嵌入到另一个自相似集中,则它们对应的迭代函数系的压缩比满足某种代数性质. |
| 关键词: 自仿嵌入 自相似集 吸引子 |
| DOI： |
| 分类号:O186.5 |
| 基金项目:Supported by National Natural Science Foundation of China (11101169). |
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| AFFINE EMBEDDINGS OF SELF-SIMILAR SETS WITH MULTI-BRANCHES |
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HUANG Ran-ran1, Yang Ya-min2
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1.School of Mathematics and Statistics, Central China Normal University, Wuhan 430079, China;2.College of Sciences, Huazhong Agriculture University, Wuhan 430070, China
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| Abstract: |
| In this paper, we consider the affine embeddings of a class of self-similar sets with multi-branches. By applying the fixed point of the contractive mapping, we show that under certain circumstances, if a self-similar set can be affinely embedded into another one, then their contractive ratios of the corresponding IFS must satisfy some arithmetric conditions. |
| Key words: affine embeddings self-similar set attractor |
