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ON SETS WHERE ITERATES OF A MEROMORPHIC FUNCTION ZIP TOWARDS INFINITY

Published online by Cambridge University Press:  23 October 2000

P. J. RIPPON  and
G. M. STALLARD
P. J. RIPPON
Affiliation:
Department of Pure Mathematics, The Open University, Walton Hall, Milton Keynes MK7 6AA
G. M. STALLARD
Affiliation:
Department of Pure Mathematics, The Open University, Walton Hall, Milton Keynes MK7 6AA
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Abstract

For a transcendental meromorphic function f, various properties of the set

formula here

were obtained in [8] and [9]. Here we establish analogous properties for the smaller sets

formula here

introduced in [5], and

formula here

We deduce a symmetry result for Julia sets J(f), and also indicate some techniques for showing that certain invariant curves lie in I′(f), Z(f) and J(f).

Type
NOTES AND PAPERS
Information
Bulletin of the London Mathematical Society , Volume 32 , Issue 5 , September 2000 , pp. 528 - 536
Copyright
© The London Mathematical Society 2000

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