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Quasiregular dynamics on the n-sphere

  • ALASTAIR N. FLETCHER (a1) and DANIEL A. NICKS (a2)
Abstract
Abstract

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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