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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2509.18202 |
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| _version_ | 1866911169266057216 |
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| author | Wang, Zhiqiang |
| author_facet | Wang, Zhiqiang |
| contents | For $0< ρ< 1/3$ and $ρ\le λ\le 1-2ρ$, let $E$ be the self-similar set generated by the iterated function system $$Φ= \big\{ φ_1(x) = ρx ,\; φ_2(x) = ρx + λ, \; φ_3(x) = ρx + 1- ρ\big\}.$$ All contractive similitudes $f$ with $f(E) \subset E$ are characterized: one can find $i_1, i_2, \ldots, i_n \in \{1,2,3\}$ such that \[ f(E)=φ_{i_1} \circ φ_{i_2} \circ \cdots \circ φ_{i_n} (E). \] |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_18202 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Self-embeddings of homogeneous self-similar sets generated by three maps Wang, Zhiqiang Dynamical Systems 28A80 For $0< ρ< 1/3$ and $ρ\le λ\le 1-2ρ$, let $E$ be the self-similar set generated by the iterated function system $$Φ= \big\{ φ_1(x) = ρx ,\; φ_2(x) = ρx + λ, \; φ_3(x) = ρx + 1- ρ\big\}.$$ All contractive similitudes $f$ with $f(E) \subset E$ are characterized: one can find $i_1, i_2, \ldots, i_n \in \{1,2,3\}$ such that \[ f(E)=φ_{i_1} \circ φ_{i_2} \circ \cdots \circ φ_{i_n} (E). \] |
| title | Self-embeddings of homogeneous self-similar sets generated by three maps |
| topic | Dynamical Systems 28A80 |
| url | https://arxiv.org/abs/2509.18202 |