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References
Beardon, A.F.: Iteration of rational functions, New York Berlin Heidelberg: Springer 1991
Becker, P.-G., Bergweiler, W.: Transcendency of local conjugacies in complex dynamics and transcendency of their values. Manuscripta Math.81, 329–337 (1993)
Borwein, P.: Hypertranscendence of the functional equationg(x)2=[g(x)2] +cx. Proc. Amer. Math. Soc.107, 215–221 (1989)
Boshernitzan, M., Rubel, L.A.: Coherent families of polynomials. Analysis6, 339–389 (1984)
Carleson, L., Gamelin, Th.W.: Complex dynamics, New York Berlin Heidelberg: Springer 1993
Carroll, F.W.: Transcendental transcendence of solutions of Schröder's equation associated with finite Blaschke products. Michigan Math. J.32, 47–57 (1985)
Fatou, M.P.: Sur les équations fonctionelles. Bull. Soc. Math. France47, 161–271 (1919);48, 33–94 (1920);48, 208–314 (1920)
Julia, G.: Memoire sur l'itération des fonctions rationelles. J. Math. Pures Appl. (7)4, 47–245 (1918)
Poincaré, H.: Sur une classe nouvelle des transcendantes uniformes. J. Math. Pures Appl. (4)6, 313–365 (1890)
Ritt, J.F.: Transcendental transcendency of certain functions of Poincaré. Math. Ann.95, 671–682 (1926)
Rubel, L.A.: Some research problems about algebraic differential equations. Trans. Amer. Math. Soc.280, 43–52 (1983)
Rubel, L.A.: Some research problems about algebraic differential equations II. Illinois J. Math.36, 659–680 (1992)
Rubel, L.A.: A survey of transcendentally transcendental functions. Amer. Math. Monthly96, 777–788 (1989)
Steinmetz, N.: Rational iteration, Berlin: Walter de Gruyter 1993
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