Literature cited
G. Valiron, Fonctions Analytiques, Presses Univ. de France, Paris (1954).
R. Nevanlinna, Eindeutige Analytische Funktionen, Springer, Berlin (1953).
A. A. Gol'dberg and I. V. Ostrovskii, The Distribution of the Values of Meromorphic Functions [in Russian], Nauka, Moscow (1970).
M. Yu. Lyubich (M. Ju. Ljubich) “Entropy properties of rational endomorphisms of the Riemann sphere,” Ergodic Theory Dynamical Systems,3, No. 3, 351–385 (1983).
A. Freire, A Lopes, and R. Mañé, “An invariant measure for rational maps,” Bol. Soc. Brasil. Mat.,14, 27–43 (1983).
P. Montel, Leçons sur les Familles Normales de Fonctions Analytiques et Leurs Applications, Gauthier-Villars, Paris (1927).
N. Yanagihara, “Exceptional values for meromorphic solutions of some difference equations,” J. Math. Soc. Jpn.,34, No. 3, 489–499 (1982).
V. S. Azarin, “On the asymptotic behavior of subharmonic functions of finite order,” Mat. Sb.,108(150), No. 2, 147–167 (1979).
M. L. Sodin, “On the distribution of the values of meromorphic functions of finite order with respect to the arguments,” Sib. Mat. Zh.,31, No. 2, 169–179 (1990).
H. Brolin, “Invariant sets under iteration of rational functions,” Ark. Mat.6, 103–144 (1965).
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Translated from Teoriya Funktsii, Funktsional'nyi Analiz i Ikh Prilozheniya, No. 53, pp. 18–25, 1990.
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Eremenko, A.É., Sodin, M.L. Iterations of rational functions and the distribution of the values of the Poincaré functions. J Math Sci 58, 504–509 (1992). https://doi.org/10.1007/BF01109688
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DOI: https://doi.org/10.1007/BF01109688