Non-escaping points of Zorich maps

TL;DR

This paper extends the understanding of the dimension of Julia sets from exponential functions to higher-dimensional Zorich maps, providing improved estimates and insights into their complex dynamics.

Contribution

It introduces new results on the dimension of radial Julia sets for quasiregular Zorich maps, advancing higher-dimensional complex dynamics research.

Findings

Improved estimates of Julia set dimensions for Zorich maps.

Extension of exponential function results to higher dimensions.

Enhanced understanding of quasiregular map dynamics.

Abstract

We extend results about the dimension of the radial Julia set of certain exponential functions to quasiregular Zorich maps in higher dimensions. Our results improve on previous estimates of the dimension also in the special case of exponential functions.