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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

On the domain of normality of an attractive fixpoint


Author: P. Bhattacharyya
Journal: Trans. Amer. Math. Soc. 153 (1971), 89-98
MSC: Primary 30.55
DOI: https://doi.org/10.1090/S0002-9947-1971-0268377-4
MathSciNet review: 0268377
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Abstract: It is proved that an entire function of order less than $ \frac{1}{2}$ has no unbounded immediate domains of attraction for any of its fixpoints. Estimates for the growth of functions with large infinite domains of attraction (e.g. including half planes) are obtained. It is shown that an entire function mapping an infinite domain into itself has polynomial growth in such domains.


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DOI: https://doi.org/10.1090/S0002-9947-1971-0268377-4
Keywords: Successor and predecessor of a point, attractive, indifferent and repulsive fixpoints, multiplier, immediate domain of attraction, domain of normality, invariant domain
Article copyright: © Copyright 1971 American Mathematical Society