The dynamics of quasiregular maps of punctured space

  title={The dynamics of quasiregular maps of punctured space},
  author={Daniel A. Nicks and D. J. Sixsmith},
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… CONTINUE READING