@article { , title = {The dynamics of quasiregular maps of punctured space}, abstract = {The Fatou-Julia iteration theory of rational and transcendental entire functions has recently been extended to quasiregular maps in more than two real dimensions. Our goal in this paper is similar; we extend the iteration theory of analytic self-maps of the punctured plane to quasiregular self-maps of punctured space. We define the Julia set as the set of points for which the complement of the forward orbit of any neighbourhood of the point is a finite set. We show that the Julia set is non-empty, and shares many properties with the classical Julia set of an analytic function. These properties are stronger than those known to hold for the Julia set of a general quasiregular map of space. We define the quasi-Fatou set as the complement of the Julia set, and generalise a result of Baker concerning the topological properties of the components of this set. A key tool in the proof of these results is a version of the fast escaping set. We generalise various results of Marti-Pete concerning this set, for example showing that the Julia set is equal to the boundary of the fast escaping set.}, doi = {10.1512/iumj.2019.68.7556}, eissn = {0022-2518}, issn = {0022-2518}, issue = {1}, journal = {Indiana University Mathematics Journal}, note = {Post-print anot allowed, PDF is allowed. Not published yet. No embargo. Letter to author to send a link to published version and CHANGE post-print to PDF. OL 26.04.2017}, pages = {323-352}, publicationstatus = {Published}, publisher = {Indiana University Mathematics Journal}, url = {https://nottingham-repository.worktribe.com/output/849441}, volume = {68}, keyword = {General Mathematics}, year = {2024}, author = {Nicks, Daniel and Sixsmith, David J.} }