Omitted values in domains of normality
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- by Walter Bergweiler and Steffen Rohde PDF
- Proc. Amer. Math. Soc. 123 (1995), 1857-1858 Request permission
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.References
- 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 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, DOI 10.1007/978-1-4612-4422-6
- 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, DOI 10.1017/CBO9780511566134
- Christian Pommerenke, Univalent functions, Studia Mathematica/Mathematische Lehrbücher, Band XXV, Vandenhoeck & Ruprecht, Göttingen, 1975. With a chapter on quadratic differentials by Gerd Jensen. MR 0507768
Additional Information
- © Copyright 1995 American Mathematical Society
- 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