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An entire function which has wandering domains

Published online by Cambridge University Press:  09 April 2009

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

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Let f(z) denote a rational or entire function of the complex variable z and fn(z), n = 1,2, …, the n−th iterate of f. Provided f is not rational of order 0 or 1, the set of those points where {fn(z)} forms a normal family is a proper subset of the plane and is invariant under the map z → f(z). A component G of is a wandering domain of f if fn(G)∩fn(G) = Ø for all k ≧ 1, n ≧ 1, k ≠ n. The paper contains the construction of a transcendental entire function which has wandering domains.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 22 , Issue 2 , September 1976 , pp. 173 - 176
Copyright
Copyright © Australian Mathematical Society 1976

References

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