Hausdorff dimension in quasiregular dynamics
Abstract
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.
- Publication:
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arXiv e-prints
- Pub Date:
- May 2022
- DOI:
- arXiv:
- arXiv:2205.03626
- Bibcode:
- 2022arXiv220503626B
- Keywords:
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- Mathematics - Dynamical Systems;
- Mathematics - Complex Variables;
- Primary 37F35;
- Secondary 30C65;
- 30D05;
- 37F10
- E-Print:
- 26 pages