Hostname: page-component-7dd5485656-g8tfn Total loading time: 0 Render date: 2025-10-31T07:05:43.788Z Has data issue: false hasContentIssue false
  • English
  • Français

The iteration of entire functions of small growth

Published online by Cambridge University Press:  24 October 2008

Gwyneth M. Stallard
Gwyneth M. Stallard
Affiliation:
Department of Mathematics, Imperial College of Science, Technology and Medicine, LondonSW7 2AZ
Get access Rights & Permissions [Opens in a new window]

Abstract

We show that if a transcendental entire function has order zero and sufficiently small growth or has order ρ < ½ and regular growth then its set of normality has no unbounded components.

Information

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 114 , Issue 1 , July 1993 , pp. 43 - 55
Copyright
Copyright © Cambridge Philosophical Society 1993

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Article purchase

Temporarily unavailable

References

REFERENCES

[1]Baker, I. N.. Zusammensetzungen ganzer Funktionen. Math. Z. 69 (1958), 121–163.CrossRefGoogle Scholar
[2]Baker, I. N.. The iteration of polynomials and transcendental entire functions. J. Austral. Math. Soc. 30 (1981), 483–495.CrossRefGoogle Scholar
[3]Cartwright, M. L.. Integral Functions (Cambridge University Press, 1965).Google Scholar
[4]Fatou, P.. Sur les equations fonctionelles. Bull. Soc. Math. France 47 (1919), 167–271Google Scholar
[4]Fatou, P.. Sur les equations fonctionelles. Bull. Soc. Math. France 48 (1920), 33–94, 208–314.CrossRefGoogle Scholar
[5]Fatou, P.. Sur l'itération des fonctions transcendantes entières. Acta. Math. 47 (1926), 337–370.CrossRefGoogle Scholar
[6]Titchmarsh, E. C.. The Theory of Functions (Oxford University Press, 1939).Google Scholar