Hausdorff dimension in quasiregular dynamics

Walter Bergweiler; Athanasios Tsantaris

doi:10.1007/s11856-024-2664-3

Hausdorff dimension in quasiregular dynamics

Dynamical Systems 2025-10-09 v1 Complex Variables

Authors: 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.

Keywords

hausdorff dimension hausdorff measure and dimension julia set

Cite

@article{arxiv.2205.03626,
  title  = {Hausdorff dimension in quasiregular dynamics},
  author = {Walter Bergweiler and Athanasios Tsantaris},
  journal= {arXiv preprint arXiv:2205.03626},
  year   = {2025}
}

Comments

26 pages

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