Uniformly quasiregular mappings of Lattès type

Mayer, Volker

doi:10.1090/S1088-4173-97-00013-1

Uniformly quasiregular mappings of Lattès type
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by Volker Mayer

Conform. Geom. Dyn. 1 (1997), 104-111

DOI: https://doi.org/10.1090/S1088-4173-97-00013-1

Published electronically: December 16, 1997

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Abstract:

Using an analogy of the Lattès’ construction of chaotic rational functions, we show that there are uniformly quasiregular mappings of the $n$-sphere $\overline {{\Bbb R}}^n$ whose Julia set is the whole sphere. Moreover there are analogues of power mappings, uniformly quasiregular mappings whose Julia set is ${\Bbb S}^{n-1}$ and its complement in ${\Bbb S}^{n}$ consists of two superattracting basins. In the chaotic case we study the invariant conformal structures and show that Lattès type rational mappings are either rigid or form a 1-parameter family of quasiconformal deformations.

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