Iteration of a class of hyperbolic

meromorphic functions

Authors:
P. J. Rippon and G. M. Stallard

Journal:
Proc. Amer. Math. Soc. **127** (1999), 3251-3258

MSC (1991):
Primary 30D05

Published electronically:
April 27, 1999

MathSciNet review:
1610785

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Abstract | References | Similar Articles | Additional Information

Abstract: We look at the class which contains those transcendental meromorphic functions for which the finite singularities of are in a bounded set and prove that, if belongs to , then there are no components of the set of normality in which as . We then consider the class which contains those functions in for which the forward orbits of the singularities of stay away from the Julia set and show (a) that there is a bounded set containing the finite singularities of all the functions and (b) that, for points in the Julia set of , the derivatives have exponential-type growth. This justifies the assertion that is a class of *hyperbolic* functions.

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Additional Information

**P. J. Rippon**

Affiliation:
Department of Pure Mathematics, The Open University, Walton Hall, Milton Keynes, MK7 6AA, England

Email:
p.j.rippon@open.ac.uk

**G. M. Stallard**

Affiliation:
Department of Pure Mathematics, The Open University, Walton Hall, Milton Keynes, MK7 6AA, England

Email:
g.m.stallard@open.ac.uk

DOI:
http://dx.doi.org/10.1090/S0002-9939-99-04942-4

Received by editor(s):
September 30, 1997

Received by editor(s) in revised form:
January 26, 1998

Published electronically:
April 27, 1999

Dedicated:
Dedicated to Professor Noel Baker on the occasion of his retirement

Communicated by:
Mary Rees

Article copyright:
© Copyright 1999
American Mathematical Society