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A non-embeddable composite of embeddable functions

Published online by Cambridge University Press:  09 April 2009

A. Ran
A. Ran
Affiliation:
Faculty of Mathematics, Technion Israel Institute of Technology, Haifa
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Let Ω be the group of the functions ƒ(z) of the complex variable z, analytic in some neighborhood of z = 0, with ƒ(0) = 0, ƒ′(0) = 1, where the group operation is the composition g[f(z)](g(z), f(z) ∈ Ω). For every function f(z) ∈ Ω there exists [4] a unique formal power series where the coefficients ƒq(s) are polynomials of the complex parameter s, with ƒ1(s) = 1, such that and, for any two complex numbers s and t, the formal law of composition is valid.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 8 , Issue 1 , February 1968 , pp. 109 - 113
Copyright
Copyright © Australian Mathematical Society 1968

References

[1]Baker, I. N., “Permutable power series and regular iteration”, J. Austral. Math. Soc. 2 (1962), 265–294.CrossRefGoogle Scholar
[2]Baker, I. N., “Fractional iteration near a fixpoint of multiplier 1”, J. Austral. Math. Soc. 4 (1964), 143–148.CrossRefGoogle Scholar
[3]Erdös, P. and Jabotinsky, E., “On analytic iteration”, J. Analyse Math. 8 (1960/1961), 361–376.CrossRefGoogle Scholar
[4]Jabotinsky, E., “On iterational invariants”, Technion, Israel Inst. Tech. Sci. Publ. 6 (1954/1955), 68–80.Google Scholar
[5]Jabotinsky, E., “Analytic iteration”, Trans. Amer. Math. Soc. 108 (1963), 457–477.CrossRefGoogle Scholar
[6]Lewin, M., “Analytic iteration of certain analytic functions”, M. Sc. Thesis, Technion, Israel Inst. Tech. Haifa (1960).Google Scholar
[7]Lewin, M., “An example of a function with non-analytic iterates”, J. Austral. Math. Soc. 5 (1965), 388–392.CrossRefGoogle Scholar
[8]Szekeres, G., “Fractional iteration of entire and rational functions”, J. Austral. Math. Soc. 4 (1964), 129–142.CrossRefGoogle Scholar