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Simultaneous Iteration by Entire or Rational Functions and Their Inverses

Part of: Entire and meromorphic functions, and related topics

Published online by Cambridge University Press:  09 April 2009

I. N. Baker  and
Zalman Rubinstein
I. N. Baker
Affiliation:
Department of Mathematics Imperial CollegeLondon S. W. 7, U. K.
Zalman Rubinstein
Affiliation:
Unversity of Michgan Ann Arbor, Machigan 48109 University of Haifa Haifa, Israel
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Abstract

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For a non-constant entire or rational function f normalized by f(0) = 0, f′(0) = 1, f″(0) ≠ 0, which is not a Möbius tranformation, the existence of a sequence is established which has the properties . The result certainly implies f(0)= |f(0)|= 1, so these conditions cannot be omitted. The condition f″ (0)≠ 0 can be replaced by f(k)(0) ≠ 0 for some k ≥ 2.

MSC classification

Secondary: 30D05: Functional equations in the complex domain, iteration and composition of analytic functions
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 34 , Issue 3 , June 1983 , pp. 364 - 367
Copyright
Copyright © Australian Mathematical Society 1983

References

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