On the quasiconformal surgery of rational functions
Shishikura, Mitsuhiro
Annales scientifiques de l'École Normale Supérieure, Tome 20 (1987), p. 1-29 / Harvested from Numdam
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     author = {Shishikura, Mitsuhiro},
     title = {On the quasiconformal surgery of rational functions},
     journal = {Annales scientifiques de l'\'Ecole Normale Sup\'erieure},
     volume = {20},
     year = {1987},
     pages = {1-29},
     doi = {10.24033/asens.1522},
     mrnumber = {88i:58099},
     zbl = {0621.58030},
     language = {en},
     url = {http://dml.mathdoc.fr/item/ASENS_1987_4_20_1_1_0}
}
Shishikura, Mitsuhiro. On the quasiconformal surgery of rational functions. Annales scientifiques de l'École Normale Supérieure, Tome 20 (1987) pp. 1-29. doi : 10.24033/asens.1522. http://gdmltest.u-ga.fr/item/ASENS_1987_4_20_1_1_0/

[1] L. Ahlfors, Lectures on Quasiconformal Mappings, Van Nostrand, 1966. | MR 34 #336 | Zbl 0138.06002

[2] V. I. Arnold, Geometrical Methods in the Theory of Ordinary Differential Equations, Springer, 1983. | MR 84d:58023 | Zbl 0507.34003

[3] P. Blanchard, Complex Analytic Dynamics on the Riemann Sphere (Bull. Amer. Math. Soc., Vol. 11, 1984, pp. 85-141). | MR 85h:58001 | Zbl 0558.58017

[4] H. Brolin, Invariant Sets Under Iteration of Rational Functions (Ark. Math., Vol. 6, 1965, pp. 103-144). | MR 33 #2805 | Zbl 0127.03401

[5] C. Camacho, On the Local Structure of Conformal Mappings and Holomorphic Vector Fields in C2 (Astérisque, Vol. 59-60, 1978, pp. 83-94). | MR 81d:58016 | Zbl 0415.30015

[6] H. Cremer, Zum Zentrumproblem (Math. Ann., Vol. 98, 1928, pp. 151-163. | JFM 53.0303.04

[7] A. Douady, Systèmes dynamiques holomorphes (Séminaire N. Bourbaki, n° 599, 1982/1983). | Numdam | Zbl 0532.30019

[8] A. Douady and J. H. Hubbard, On the Dynamics of Polynomial-Like Mappings (Ann. scient. Éc. Norm. Sup., 4th Serie, T. 18, 1985, pp. 287-343). | Numdam | MR 87f:58083 | Zbl 0587.30028

[9] P. Fatou, Sur les équations fonctionnelles (Bull. Soc. Math. Fr., Vol. 47, 1919, pp. 161-271 ; Vol. 48, 1920, pp. 33-94 et pp. 208-304). | JFM 47.0921.02 | Numdam | Numdam

[10] M. R. Herman, Exemples de fractions rationnelles ayant une orbite dense sur la sphère de Riemann (Bull. Soc. Math. Fr., Vol. 112, 1984, pp. 93-142). | Numdam | MR 86d:58055 | Zbl 0559.58020

[11] M. R. Herman, Are There Critical Points on the Boundaries of Singular Domains ? (Commun. Math. Phys., Vol. 99, 1985, pp. 593-612). | MR 86j:58067 | Zbl 0587.30040

[12] G. Julia, Mémoire sur l'itération des fonctions rationnelles (J. Math. pures et appl., Vol. 8, 1918, pp. 47-245). | JFM 46.0520.06

[13] O. Lehto and K. Virtanen, Quasiconformal Mappings in the Plane, Springer-Verlag, 1973. | MR 49 #9202 | Zbl 0267.30016

[14] R. Mañ;É, P. Sad and D. Sullivan, On the Dynamics of Rational Maps (Ann. scient. Éc. Norm. Sup., 4th Serie, T. 16, 1983. pp. 193-217). | Numdam | MR 85j:58089 | Zbl 0524.58025

[15] C. L. Siegel, Iteration of Analytic Functions (Ann. of Math., Vol. 43, 1942, pp. 607-612). | MR 4,76c | Zbl 0061.14904

[16] M. Shishikura, Surgery of Complex Analytic Dynamical systems, Dynamical Systems and Nonlinear Oscillations, G. Ikegami Ed., World Scientific Advanced Series in Dynamical Systems, Vol. 1, World Scientific, 1986, pp. 93-105.

[17] D. Sullivan, Quasiconformal Homeomorphisms and Dynamics I, III, preprint I.H.E.S.