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Iterates of meromorphic functions: I

Published online by Cambridge University Press:  19 September 2008

I. N. Baker ,
J. Kotus  and
Lü Yinian
I. N. Baker
Affiliation:
Mathematics Dept., Imperial College, London SW7 2AX, UK
J. Kotus
Affiliation:
Institute of Mathematics, Technical University of Warsaw, 00–661 Warsaw, Poland
Lü Yinian
Affiliation:
Institute of Mathematics, Academia Sinica, Beijing, China
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Abstract

For functions meromorphic in the plane, apart from an exceptional case, the Julia set J is the closure of the set of all preimages of poles. The repelling periodic cycles are dense in J. In contrast with the case of transcendental entire functions, J may be a subset of a straight line and general classes of functions for which this is the case can be determined. J may also lie on a quasicircle through infinity which is not a straight line.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 11 , Issue 2 , June 1991 , pp. 241 - 248
Copyright
Copyright © Cambridge University Press 1991

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References

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