Attractor sets and Julia sets in low dimensions
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arXiv
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| Format: | Preprint |
| Published: |
2018
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| _version_ | 1866908441087311872 |
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| author | Fletcher, A. |
| author_facet | Fletcher, A. |
| contents | If $X$ is the attractor set of a conformal IFS in dimension two or three, we prove that there exists a quasiregular semigroup $G$ with Julia set equal to $X$. We also show that in dimension two, with a further assumption similar to the open set condition, the same result can be achieved with a semigroup generated by one element. Consequently, in this case the attractor set is quasiconformally equivalent to the Julia set of a rational map. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_1810_02834 |
| institution | arXiv |
| publishDate | 2018 |
| record_format | arxiv |
| spellingShingle | Attractor sets and Julia sets in low dimensions Fletcher, A. Complex Variables Dynamical Systems If $X$ is the attractor set of a conformal IFS in dimension two or three, we prove that there exists a quasiregular semigroup $G$ with Julia set equal to $X$. We also show that in dimension two, with a further assumption similar to the open set condition, the same result can be achieved with a semigroup generated by one element. Consequently, in this case the attractor set is quasiconformally equivalent to the Julia set of a rational map. |
| title | Attractor sets and Julia sets in low dimensions |
| topic | Complex Variables Dynamical Systems |
| url | https://arxiv.org/abs/1810.02834 |