Hausdorff dimension in quasiregular dynamics
Fuente:
arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2022
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| _version_ | 1866915537040179200 |
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| author | Bergweiler, Walter Tsantaris, Athanasios |
| author_facet | Bergweiler, Walter Tsantaris, Athanasios |
| contents | It is shown that the Hausdorff dimension of the fast escaping set of a quasiregular self-map of ${\mathbb R}^3$ can take any value in the interval $[1,3]$. The Hausdorff dimension of the Julia set of such a map is estimated under some growth condition. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2205_03626 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Hausdorff dimension in quasiregular dynamics Bergweiler, Walter Tsantaris, Athanasios Dynamical Systems Complex Variables Primary 37F35, Secondary 30C65, 30D05, 37F10 It is shown that the Hausdorff dimension of the fast escaping set of a quasiregular self-map of ${\mathbb R}^3$ can take any value in the interval $[1,3]$. The Hausdorff dimension of the Julia set of such a map is estimated under some growth condition. |
| title | Hausdorff dimension in quasiregular dynamics |
| topic | Dynamical Systems Complex Variables Primary 37F35, Secondary 30C65, 30D05, 37F10 |
| url | https://arxiv.org/abs/2205.03626 |