Geodesic
Fractional iterates of functions analytic in the unit disk, with given fixed points
Sbornik. Mathematics, Tome 74 (1993) no. 1, pp. 29-46 Cet article a éte moissonné depuis la source Math-Net.Ru

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An infinitesimal description is obtained for fractional iterates of analytic functions on the unit disk under the condition that the functions and their iterates do not move fixed points on the unit circle at which they have finite angular derivatives. 
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V. V. Goryainov. Fractional iterates of functions analytic in the unit disk, with given fixed points. Sbornik. Mathematics, Tome 74 (1993) no. 1, pp. 29-46. http://geodesic.mathdoc.fr/item/SM_1993_74_1_a2/

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