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 | References | Similar Articles | Additional Information
Abstract: It is proved that an entire function of order less than 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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Additional Information
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