Iteration of Quasiregular Mappings

Complex dynamics is the study of iteration of analytic functions on the complex plane. This has been a remarkably active area of research in recent years. A rich mathematical structure is seen to emerge amidst the chaotic behaviour. Its appeal is enhanced by the intricate nature of the Julia sets that arise, and fascinating images of these fractal sets are widely admired. Quasiregular mappings of n-dimensional real space generalise analytic functions on the complex plane. One can therefore attempt to develop a theory of quasiregular iteration parallel to the results of complex dynamics. Such a theory is just beginning to emerge, lying between the well-studied analytic case (where many powerful tools are available) and general iteration in several real variables, which is much less well-understood.