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Infinite limits in the iteration of entire functions

Published online by Cambridge University Press:  19 September 2008

I. N. Baker
I. N. Baker
Affiliation:
Department of Mathematics, Imperial College of Science and Technology, London SW7 2BZ, England
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Abstract

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If f is a transcendental entire function and D is a non-wandering component of the set of normality of the iterates of f such that fn → ∞ in D then log |fn(z)| = O(n) as n → ∞ for z in D. For a wandering component the convergence of fn to ∞ in D may be arbitrarily fast.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 8 , Issue 4 , December 1988 , pp. 503 - 507
Copyright
Copyright © Cambridge University Press 1988

References

REFERENCES

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