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Permutable power series and regular iteration

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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If f(z) is a power series convergent for |z| < ρ, where ρ > 0, then f(z) is said to have a fixpoint of multiplir a1 at z = 0. In the (local) iteration of f(z) one studies the sequence {fn(z)}, n = 0, 1, 2, … in a neighbourhood of z = 0, fn(z) benig defined by For many values of the multiplier a1, including 0 < |a1| < 1 and |a1| > 1, the local iteration of f(z) is completely mastered by the introduction of Schröder's functional equation.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 2 , Issue 3 , February 1962 , pp. 265 - 294
Copyright
Copyright © Australian Mathematical Society 1962

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