Hausdorff dimension in quasiregular dynamics

2022/05/07 by Bergweiler, Walter, Tsantaris, Athanasios · 1 citation
#30D05 #37F10 #Complex Variables (math.CV) #Dynamical Systems (math.DS) #FOS: Mathematics #Primary 37F35 #Secondary 30C65

paper · doi:10.48550/arxiv.2205.03626

Abstract

It is shown that the Hausdorff dimension of the fast escaping set of a quasiregular self-map of \mathbb R³ 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.

Cited by

• The escaping set in transcendental dynamics

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