Superattracting fixed points of quasiregular mappings
Fletcher, Alastair and Nicks, Daniel A. (2016) Superattracting fixed points of quasiregular mappings. Ergodic Theory and Dynamical Systems, 36 (3). pp. 781-793. ISSN 1469-4417
Official URL: http://journals.cambridge.org/action/displayAbstract?fromPage=online&aid=10264173&fileId=S0143385714000881
We investigate the rate of convergence of the iterates of an n-dimensional quasiregular mapping within the basin of attraction of a fixed point of high local index. A key tool is a refinement 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 infinity.
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