Ergodic Theory and Dynamical Systems

Research Article

Quasiregular dynamics on the n-sphere

ALASTAIR N. FLETCHERa1 and DANIEL A. NICKSa2

a1 Mathematics Institute, University of Warwick, Coventry CV4 7AL, UK (email: Alastair.Fletcher@warwick.ac.uk)

a2 School of Mathematical Sciences, University of Nottingham, Nottingham NG7 2RD, UK (email: Dan.Nicks@maths.nottingham.ac.uk)

Abstract

In this paper, we investigate the boundary of the escaping set I(f) for quasiregular mappings on ℝn, both in the uniformly quasiregular case and in the polynomial type case. The aim is to show that ∂I(f) is the Julia set J(f) when the latter is defined, and shares properties with the Julia set when J(f) is not defined.

(Received September 02 2009)

(Revised October 09 2009)

(Online publication January 18 2010)