Quasiregular dynamics on the n-sphere

Fletcher, Alastair N. and Nicks, Daniel (2011). Quasiregular dynamics on the n-sphere. Ergodic Theory and Dynamical Systems, 31(1) pp. 23–31.

DOI: https://doi.org/10.1017/S0143385709001072

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.

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