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Iterations of rational functions and the distribution of the values of the Poincaré functions

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Literature cited

  1. G. Valiron, Fonctions Analytiques, Presses Univ. de France, Paris (1954).

    Google Scholar 

  2. R. Nevanlinna, Eindeutige Analytische Funktionen, Springer, Berlin (1953).

    Google Scholar 

  3. A. A. Gol'dberg and I. V. Ostrovskii, The Distribution of the Values of Meromorphic Functions [in Russian], Nauka, Moscow (1970).

    Google Scholar 

  4. 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).

    Google Scholar 

  5. A. Freire, A Lopes, and R. Mañé, “An invariant measure for rational maps,” Bol. Soc. Brasil. Mat.,14, 27–43 (1983).

    Google Scholar 

  6. P. Montel, Leçons sur les Familles Normales de Fonctions Analytiques et Leurs Applications, Gauthier-Villars, Paris (1927).

    Google Scholar 

  7. N. Yanagihara, “Exceptional values for meromorphic solutions of some difference equations,” J. Math. Soc. Jpn.,34, No. 3, 489–499 (1982).

    Google Scholar 

  8. V. S. Azarin, “On the asymptotic behavior of subharmonic functions of finite order,” Mat. Sb.,108(150), No. 2, 147–167 (1979).

    Google Scholar 

  9. 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).

    Google Scholar 

  10. H. Brolin, “Invariant sets under iteration of rational functions,” Ark. Mat.6, 103–144 (1965).

    Google Scholar 

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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

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