Superattracting fixed points of quasiregular mappings

  title={Superattracting fixed points of quasiregular mappings},
  author={Alastair N. Fletcher and Daniel A. Nicks},
We investigate the rate of convergence of the iterates of an n-dimensional quasiregular mapping within the basin of attraction of a xed point of high local index. A key tool is a re nement of a result that gives bounds on the distortion of the image of a small spherical shell. This result also has applications to the rate of growth of quasiregular mappings of polynomial type, and to the rate at which the iterates of such maps can escape to in nity.