Superattracting fixed points of quasiregular mappings

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...

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Bibliographic Details
Published inErgodic theory and dynamical systems Vol. 36; no. 3; pp. 781 - 793
Main Authors FLETCHER, ALASTAIR, NICKS, DANIEL A.
Format Journal Article
LanguageEnglish
Published Cambridge, UK Cambridge University Press 01.05.2016
Subjects
Basins
Convergence
Distortion
Dynamical systems
Mapping
Mathematics
Polynomials
Spherical shells
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Summary: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.
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
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content type line 23
ISSN:0143-3857
1469-4417
DOI:10.1017/etds.2014.88