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    FLETCHER, ALASTAIR and FRYER, ROB 2016. Dynamics of quasiregular mappings with constant complex dilatation. Ergodic Theory and Dynamical Systems, Vol. 36, Issue. 02, p. 514.

    FLETCHER, ALASTAIR and NICKS, DANIEL A. 2016. Superattracting fixed points of quasiregular mappings. Ergodic Theory and Dynamical Systems, Vol. 36, Issue. 03, p. 781.

    Fletcher, Alastair and Wu, Jang-Mei 2015. Julia sets and wild Cantor sets. Geometriae Dedicata, Vol. 174, Issue. 1, p. 169.

    Bergweiler, Walter and Nicks, Daniel A. 2014. Foundations for an iteration theory of entire quasiregular maps. Israel Journal of Mathematics, Vol. 201, Issue. 1, p. 147.

    Bergweiler, Walter Drasin, David and Fletcher, Alastair 2014. The fast escaping set for quasiregular mappings. Analysis and Mathematical Physics, Vol. 4, Issue. 1-2, p. 83.

    Bergweiler, Walter Fletcher, Alastair and Nicks, Daniel A. 2014. The Julia Set and the Fast Escaping Set of a Quasiregular Mapping. Computational Methods and Function Theory, Vol. 14, Issue. 2-3, p. 209.

    BERGWEILER, WALTER 2013. Fatou–Julia theory for non-uniformly quasiregular maps. Ergodic Theory and Dynamical Systems, Vol. 33, Issue. 01, p. 1.

    Fletcher, Alastair N. and Nicks, Daniel A. 2013. Chaotic dynamics of a quasiregular sine mapping. Journal of Difference Equations and Applications, Vol. 19, Issue. 8, p. 1353.

    Bergweiler, Walter 2011. Iteration of Quasiregular Mappings. Computational Methods and Function Theory, Vol. 10, Issue. 2, p. 455.

    FLETCHER, ALASTAIR N. and NICKS, DANIEL A. 2011. Julia sets of uniformly quasiregular mappings are uniformly perfect. Mathematical Proceedings of the Cambridge Philosophical Society, Vol. 151, Issue. 03, p. 541.


Quasiregular dynamics on the n-sphere

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  • Published online: 18 January 2010

In this paper, we investigate the boundary of the escaping set I(f) for quasiregular mappings on ℝn, both in the uniformly quasiregular case and in the polynomial type case. The aim is to show that ∂I(f) is the Julia set J(f) when the latter is defined, and shares properties with the Julia set when J(f) is not defined.

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[1]A. F. Beardon . Iteration of Rational Functions (Graduate Texts in Mathematics, 132). Springer, New York, 1991.

[2]W. Bergweiler . Iteration of meromorphic functions. Bull. Amer. Math. Soc. 29 (1993), 151188.

[5]W. Bergweiler , A. Fletcher , J. Langley and J. Meyer . The escaping set of a quasiregular mapping. Proc. Amer. Math. Soc. 137(2) (2009), 641651.

[13]V. Mayer . Uniformly quasiregular mappings of Lattès type. Conform. Geom. Dyn. 1 (1997), 104111.

[16]R. Miniowitz . Normal families of quasimeromorphic mappings. Proc. Amer. Math. Soc. 84(1) (1982), 3543.

[18]S. Rickman . Quasiregular Mappings (Ergebnisse der Mathematik und ihrer Grenzgebiete, 26). Springer, Berlin, 1993.

[20]H. Siebert . Fixed points and normal families of quasiregular mappings. J. Anal. Math. 98 (2006), 145168.

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Ergodic Theory and Dynamical Systems
  • ISSN: 0143-3857
  • EISSN: 1469-4417
  • URL: /core/journals/ergodic-theory-and-dynamical-systems
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