Omitted values in domains of normality
Authors:
Walter Bergweiler and Steffen Rohde
Journal:
Proc. Amer. Math. Soc. 123 (1995), 1857-1858
MSC:
Primary 30D05; Secondary 30D20
DOI:
https://doi.org/10.1090/S0002-9939-1995-1249869-X
MathSciNet review:
1249869
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Abstract | References | Similar Articles | Additional Information
Abstract: It is proved that if U and V are connected components of the Fatou set of an entire function f and if $f(U) \subset V$, then $V\backslash f(U)$ contains at most one point.
- I. N. Baker, Wandering domains in the iteration of entire functions, Proc. London Math. Soc. (3) 49 (1984), no. 3, 563–576. MR 759304, DOI https://doi.org/10.1112/plms/s3-49.3.563
- Alan F. Beardon, Iteration of rational functions, Graduate Texts in Mathematics, vol. 132, Springer-Verlag, New York, 1991. Complex analytic dynamical systems. MR 1128089
- E. F. Collingwood and A. J. Lohwater, The theory of cluster sets, Cambridge Tracts in Mathematics and Mathematical Physics, No. 56, Cambridge University Press, Cambridge, 1966. MR 0231999
- Christian Pommerenke, Univalent functions, Vandenhoeck & Ruprecht, Göttingen, 1975. With a chapter on quadratic differentials by Gerd Jensen; Studia Mathematica/Mathematische Lehrbücher, Band XXV. MR 0507768
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Additional Information
Keywords:
Iteration,
entire function,
set of normality,
Fatou set,
Julia set
Article copyright:
© Copyright 1995
American Mathematical Society
