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arXiv · 2205.03626

Hausdorff dimension in quasiregular dynamics

Walter Bergweiler·Athanasios Tsantaris
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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.

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Walter Bergweiler, Athanasios Tsantaris. 2022-05-07. Hausdorff dimension in quasiregular dynamics. https://doi.org/10.1007/s11856-024-2664-3

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