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Fractional iteration near a fixpoint of multiplier 1.

Published online by Cambridge University Press:  09 April 2009

I. N. Baker
I. N. Baker
Affiliation:
Imperial College of Science and Technology, London.
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An analytic function f(z) is said to have a fixpoint ξ ≠ ∞ of multiplier 1 if f(ξ) = ξ, f'(ξ) = 1. The function then has an expansion .

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 4 , Issue 2 , May 1964 , pp. 143 - 148
Copyright
Copyright © Australian Mathematical Society 1964

References

[1]Baker, I. N., Permutable power series and regular iteration, J. Australian Math. Soc. 2 (1962), 265–294.CrossRefGoogle Scholar
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[3]Fatou, P., Sur l'itération des fonctions transcendantes entières, Acta Math. 47, 337–370 (1926).CrossRefGoogle Scholar
[4]Szekeres, G., Fractional iteration of entire and rational functions, this Journal 4 (1964), 129–142.Google Scholar