Geodesic
Fractional iterates of functions analytic in the unit disk, with given fixed points
Sbornik. Mathematics, Tome 74 (1993) no. 1, pp. 29-46 
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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Voir la notice de l'article provenant de la source Math-Net.Ru

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.

[1] Schroeder H., “Uber itierte Funktionen”, Math. Ann., 3 (1871), 296–322 | DOI

[2] Koenigs G., “Recherches sur les intégrales des certaines equations fonctionelles”, Ann. Ecole Norm. Sup., 1(3) (1884), 3–41 | MR | Zbl

[3] Hadamard J., “Two works on iteration and related questions”, Bull. Amer. Math. Soc., 50 (1944), 67–75 | DOI | MR | Zbl

[4] Cowen C. C., “Iteration and the solution of functional equations analytic in the unit disk”, Trans. Amer. Math. Soc., 265 (1981), 69–95 | DOI | MR | Zbl

[5] Kharris T., Teoriya vetvyaschikhsya sluchainykh protsessov, Mir, M., 1966

[6] Sevastyanov B. A., Vetvyaschiesya protsessy, Nauka, M., 1971 | MR

[7] Berkson E., Porta H., “Semigroups of analytic functions and composition operators”, Michigan Math. J., 25 (1978), 101–115 | DOI | MR | Zbl

[8] Goryainov V. V., “Polugruppy konformnykh otobrazhenii”, Matem. sb., 129(171) (1986), 451–472 | MR | Zbl

[9] Denjov A., “Sur l'iteration des fonctions analytiques”, C.R. Acad. Sci. Paris Sér. A, 182 (1926), 255–257

[10] Wolff J., “Sur l'iteration des fonctions”, C.R. Acad. Sci. Paris Sér. A, 182 (1926), 42–43 ; 200–201 | Zbl | Zbl

[11] Nevanlinna R., Odnoznachnye analiticheskie funktsii, OGIZ, M.–L., 1941

[12] Pommerenke Ch., Univalent functions, Vandenhoeck and Ruprecht, Göttingen, 1975 | MR | Zbl

[13] Khille E., Fillips R., Funktsionalnyi analiz i polugruppy, IL, M., 1962

[14] Natanson I. P., Teoriya funktsii veschestvennoi peremennoi, Nauka, M., 1974 | MR

[15] Duren P. L., Univalent functions, Springer-Verlag, New York, 1983 | MR | Zbl

[16] Ahlfors L. V., Conformal invariants. Topics in Geometric function theory, McGraw-Hill Book Company, New York, 1973 | MR | Zbl