Geodesic
Koenigs function and fractional iterates of probability generating functions
Sbornik. Mathematics, Tome 193 (2002) no. 7, pp. 1009-1025

Voir la notice de l'article provenant de la source Math-Net.Ru

The Koenigs function arises as the limit of an appropriately normalized sequence of iterates of holomorphic functions. On the other hand it is a solution of a certain functional equation and can be used for the definition of iterates of the original function. A description of the class of Koenigs functions corresponding to probability generating functions embeddable in a one-parameter group of fractional iterates is provided. The results obtained can be regarded as a test for the embeddability of a Galton–Watson process in a homogeneous Markov branching process. 
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     author = {V. V. Goryainov},
     title = {Koenigs function and fractional iterates of probability generating functions},
     journal = {Sbornik. Mathematics},
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     url = {http://geodesic.mathdoc.fr/item/SM_2002_193_7_a2/}
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V. V. Goryainov. Koenigs function and fractional iterates of probability generating functions. Sbornik. Mathematics, Tome 193 (2002) no. 7, pp. 1009-1025. http://geodesic.mathdoc.fr/item/SM_2002_193_7_a2/