On the domain of normality of an attractive fixpoint

Bhattacharyya, P.

doi:10.1090/S0002-9947-1971-0268377-4

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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