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The section [[Iterated_function#Some_formulas_for_fractional_iteration|Some formulas for fractional iteration]] is very similar to my own unpublished results. My question is, can anyone verify the formulas are in a peer reviewed published work? [[User:Daniel Geisler|Daniel Geisler]] ([[User talk:Daniel Geisler|talk]]) 20:21, 13 May 2014 (UTC)
:My notes too, of course. '''''Please sign your posts'''''. You are referring to the off-the-bat power series expansion around a fixed point that, I trust, you saw in the History of the article, [[User:Drschawrz]] adduced in August 2011? This is the frontal--and inefficient--assault to the problem, that, mercifully, Schroeder has provided the more systematic solution to a century and a half ago. Try reproducing his results on the table of section 9 (Examples) that way! Conjugacy is of course the way to go. Most standard courses on iterated functions and textbooks have, naturally, one version of them or another. You are unhappy with the Carleson and Gamelin 1993 text? [[User:Cuzkatzimhut|Cuzkatzimhut]] ([[User talk:Cuzkatzimhut|talk]]) 00:22, 14 May 2014 (UTC)
::The issue is whether the Taylors series can be validated by a peer reviewed article in a published journal. Am I unhappy with the Carleson and Gamelin 1993 text? Actually I contacted one of the authors and he said he no longer worked with complex dynamics. My concern is that while the Classification of Fixed Points documents the Schroeder and Abel equations, it does it in a round about way and provides no explanation of why they are necessary. The power series expansion around a fixed point has interesting combinatorial properties besides providing a natural explanation for both the Schroeder and Abel equations. [[User:Daniel Geisler|Daniel Geisler]] ([[User talk:Daniel Geisler|talk]]) 06:54, 14 May 2014 (UTC)
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