Geodesic
Koenigs Function and Fractional Iteration of Functions Analytic in the Unit Disk with Real Coefficients and Fixed Points
Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, Tome 13 (2013) no. 1, pp. 67-71

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The present paper deals with the problem of fractional iteration of functions analytic in the unit disk, with real Taylor's coefficients. It is assumed that there exist interior and boundary fixed points. The solution is given in terms of the Koenigs function. 
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     author = {O. S. Kudryavtseva},
     title = {Koenigs {Function} and {Fractional} {Iteration} of {Functions} {Analytic} in the {Unit} {Disk} with {Real} {Coefficients} and {Fixed} {Points}},
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O. S. Kudryavtseva. Koenigs Function and Fractional Iteration of Functions Analytic in the Unit Disk with Real Coefficients and Fixed Points. Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, Tome 13 (2013) no. 1, pp. 67-71. http://geodesic.mathdoc.fr/item/ISU_2013_13_1_a16/