Some examples of Baker domains

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Published 13 March 2012 • 2012 IOP Publishing Ltd & London Mathematical Society
, , Citation Walter Bergweiler and Jian-Hua Zheng 2012 Nonlinearity 25 1033 DOI 10.1088/0951-7715/25/4/1033

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Author affiliations

1 Mathematisches Seminar, Christian-Albrechts-Universität zu Kiel, Ludewig-Meyn-Str. 4, 24098 Kiel, Germany

2 Department of Mathematical Sciences, Tsinghua University, People's Republic of China

Dates

  1. Received 6 October 2011
  2. Published

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0951-7715/25/4/1033

Abstract

We construct entire functions with hyperbolic and simply parabolic Baker domains on which the functions are not univalent. The Riemann maps from the unit disc to these Baker domains extend continuously to certain arcs on the unit circle. The results answer questions posed by Fagella and Henriksen, Baker and Domínguez, and others.

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10.1088/0951-7715/25/4/1033