On the quasiconformal surgery of rational functions

Mitsuhiro Shishikura

Annales scientifiques de l'École Normale Supérieure (1987)

  • Volume: 20, Issue: 1, page 1-29
  • ISSN: 0012-9593

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Shishikura, Mitsuhiro. "On the quasiconformal surgery of rational functions." Annales scientifiques de l'École Normale Supérieure 20.1 (1987): 1-29. <http://eudml.org/doc/82191>.

@article{Shishikura1987,
author = {Shishikura, Mitsuhiro},
journal = {Annales scientifiques de l'École Normale Supérieure},
keywords = {periodic point; stable region; rational map; nonrepelling cycles; attractive basins; parabolic basins; Herman rings},
language = {eng},
number = {1},
pages = {1-29},
publisher = {Elsevier},
title = {On the quasiconformal surgery of rational functions},
url = {http://eudml.org/doc/82191},
volume = {20},
year = {1987},
}

TY - JOUR
AU - Shishikura, Mitsuhiro
TI - On the quasiconformal surgery of rational functions
JO - Annales scientifiques de l'École Normale Supérieure
PY - 1987
PB - Elsevier
VL - 20
IS - 1
SP - 1
EP - 29
LA - eng
KW - periodic point; stable region; rational map; nonrepelling cycles; attractive basins; parabolic basins; Herman rings
UR - http://eudml.org/doc/82191
ER -

References

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  1. [1] L. AHLFORS, Lectures on Quasiconformal Mappings, Van Nostrand, 1966. Zbl0138.06002MR34 #336
  2. [2] V. I. ARNOLD, Geometrical Methods in the Theory of Ordinary Differential Equations, Springer, 1983. Zbl0507.34003MR84d:58023
  3. [3] P. BLANCHARD, Complex Analytic Dynamics on the Riemann Sphere (Bull. Amer. Math. Soc., Vol. 11, 1984, pp. 85-141). Zbl0558.58017MR85h:58001
  4. [4] H. BROLIN, Invariant Sets Under Iteration of Rational Functions (Ark. Math., Vol. 6, 1965, pp. 103-144). Zbl0127.03401MR33 #2805
  5. [5] C. CAMACHO, On the Local Structure of Conformal Mappings and Holomorphic Vector Fields in C2 (Astérisque, Vol. 59-60, 1978, pp. 83-94). Zbl0415.30015MR81d:58016
  6. [6] H. CREMER, Zum Zentrumproblem (Math. Ann., Vol. 98, 1928, pp. 151-163. JFM53.0303.04
  7. [7] A. DOUADY, Systèmes dynamiques holomorphes (Séminaire N. Bourbaki, n° 599, 1982/1983). Zbl0532.30019
  8. [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). Zbl0587.30028MR87f:58083
  9. [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). Zbl47.0921.02JFM47.0921.02
  10. [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). Zbl0559.58020MR86d:58055
  11. [11] M. R. HERMAN, Are There Critical Points on the Boundaries of Singular Domains ? (Commun. Math. Phys., Vol. 99, 1985, pp. 593-612). Zbl0587.30040MR86j:58067
  12. [12] G. JULIA, Mémoire sur l'itération des fonctions rationnelles (J. Math. pures et appl., Vol. 8, 1918, pp. 47-245). Zbl46.0520.06JFM46.0520.06
  13. [13] O. LEHTO and K. VIRTANEN, Quasiconformal Mappings in the Plane, Springer-Verlag, 1973. Zbl0267.30016MR49 #9202
  14. [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). Zbl0524.58025MR85j:58089
  15. [15] C. L. SIEGEL, Iteration of Analytic Functions (Ann. of Math., Vol. 43, 1942, pp. 607-612). Zbl0061.14904MR4,76c
  16. [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. [17] D. SULLIVAN, Quasiconformal Homeomorphisms and Dynamics I, III, preprint I.H.E.S. 

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