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.

26 pages

References in corpus (1)

• The escaping set of a quasiregular mapping

Cited by in corpus (1)

• The escaping set in transcendental dynamics