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Quasiregular analogues of critically finite rational functions with parabolic orbifold

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Abstract

We study uniformly quasiregular mappings of\(\bar {\mathbb{R}}^n \), i.e., quasiregular mappingsf with uniform control of the dilatation of all the iteratesf k, which are analogues of critically finite rational functions with parabolic orbifold. They form a rich family of non-injective uniformly quasiregular mappings. In our main result we characterize them among all uniformly quasiregular mappings as those which have an invariant conformal structure flat at a point of a repelling cycle.

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Authors and Affiliations

  1. U.R.A. 751 UFR de Mathématiques Pures et Appliquées, Université de Lille I, 59655, Villeneuve d’Ascq, Cedex, France

    Volker Mayer

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  1. Volker Mayer
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Correspondence to Volker Mayer.

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Mayer, V. Quasiregular analogues of critically finite rational functions with parabolic orbifold. J. Anal. Math. 75, 105–119 (1998). https://doi.org/10.1007/BF02788694

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  • DOI: https://doi.org/10.1007/BF02788694

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