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On the existence of fixpoints of composite meromorphic functions

Author: Walter Bergweiler
Journal: Proc. Amer. Math. Soc. 114 (1992), 879-880
MSC: Primary 30D05
MathSciNet review: 1091176
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Abstract: Let $ f$ be a meromorphic function with at least two poles, and let $ g$ be an entire transcendental function. It is proved that the composite function $ f \circ g$ has infinitely many fixpoints.

References [Enhancements On Off] (What's this?)

  • [1] W. Bergweiler, Proof of a conjecture of Gross concerning fix-points, Math. Z. 204 (1990), 381-390. MR 1107470 (92j:30028)
  • [2] F. Gross, On factorization of meromorphic functions, Trans. Amer. Math. Soc. 131 (1968), 215-222. MR 0220936 (36:3988)
  • [3] -Factorization of meromorphic functions, U.S. Government Printing Office, Washington, DC, 1972.

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Keywords: Entire function, meromorphic function, composite function, fixpoint
Article copyright: © Copyright 1992 American Mathematical Society

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