Exemples de fractions rationnelles ayant une orbite dense sur la sphère de Riemann

Michael R. Herman

Bulletin de la Société Mathématique de France (1984)

  • Volume: 112, page 93-142
  • ISSN: 0037-9484

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Herman, Michael R.. "Exemples de fractions rationnelles ayant une orbite dense sur la sphère de Riemann." Bulletin de la Société Mathématique de France 112 (1984): 93-142. <http://eudml.org/doc/87475>.

@article{Herman1984,
author = {Herman, Michael R.},
journal = {Bulletin de la Société Mathématique de France},
keywords = {rational functions with dense orbits; singular domains; constant rotation number},
language = {fre},
pages = {93-142},
publisher = {Société mathématique de France},
title = {Exemples de fractions rationnelles ayant une orbite dense sur la sphère de Riemann},
url = {http://eudml.org/doc/87475},
volume = {112},
year = {1984},
}

TY - JOUR
AU - Herman, Michael R.
TI - Exemples de fractions rationnelles ayant une orbite dense sur la sphère de Riemann
JO - Bulletin de la Société Mathématique de France
PY - 1984
PB - Société mathématique de France
VL - 112
SP - 93
EP - 142
LA - fre
KW - rational functions with dense orbits; singular domains; constant rotation number
UR - http://eudml.org/doc/87475
ER -

References

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  1. [A] ARNOLD (V. I.). — On the mappings of the circumference onto itself, Translations A.M.S., vol. 46, 2nd series, p. 213-284. Zbl0152.41905
  2. [B] BROLIN (H.). — Invariant sets under iteration of rational functions, Arkiv för Mathematik, vol. 6, 1966, p. 103-144. Zbl0127.03401MR33 #2805
  3. [B1] BRJUNO (A. D.). — Analytical form of differential equations, Trans. Moscow Math. Soc., vol. 25, 1971, p. 131-288. Zbl0272.34018MR51 #13365
  4. [B2] BAKER (I. N.). — An entire function which has wandering domains, J. Austral. Math. Soc., vol. 22, 1976, p. 173-176. Zbl0335.30001MR54 #7777
  5. [C] CHERRY (T. M.). — A singular case of iteration of analytic functions: A contribution to small divisor problem, in Nonlinear Problems of Engineering, Academic Press, New York, 1964, p. 29-50. Zbl0143.29401MR31 #2383
  6. [CH] CHOQUET (G.). — Lectures on analysis, vol. I, Benjamin Inc., 1969. 
  7. [C1] CREMER (H.). — Zum Zentrumproblem, Math. Ann., vol. 98, 1928, p. 151-163. JFM53.0303.04
  8. [C2] CREMER (H.). — Über die Schrödersche funktionalgleichung und das Schwarscher Eckenabbildungsproblem, Ber. Math. Phys. Klasse der Sächs Akad. Wiss. Leipzig, vol. 84, 1932, p. 291-324. Zbl0007.16902JFM58.0327.02
  9. [D] DOUADY (A.). — Systèmes dynamiques holomorphes, Séminaire N. Bourbaki, n° 599, vol. 1982-1983, Astérisque, vol. 104-105, S.M.F., 1983, p. 39-63. Zbl0532.30019MR85h:58090
  10. [F-H] FATHI (A.) et HERMAN (M.). — Existence de difféomorphismes minimaux, Astérisque, vol. 49, 1977, p. 37-59. Zbl0374.58010MR58 #2889
  11. [F] FATOU (P.). — Mémoires sur les équations fonctionnelles, Bull. S.M.F., vol. 47, 1919, p. 161-271 et vol. 48, 1920, p. 33-94, p. 208-304. Zbl47.0921.02JFM47.0921.02
  12. [H1] HELSON (H.) et SARASON (D.). — Past and future, Math. Scand., vol. 21, 1967, p. 5-16. Zbl0241.60029MR38 #5282
  13. [H] HERMAN (M.). — Sur la conjugaison différentiable des difféomorphismes du cercle à des rotations, Pub. Math. I.H.E.S., vol. 49, 1979, p. 5-233. Zbl0448.58019MR81h:58039
  14. [L] LANG (S.). — Elliptic functions, Addison-Wesley, 1973. Zbl0316.14001MR53 #13117
  15. [LA] LATTÈS (S.). — Sur l'itération des substitutions rationnelles et les fonctions de Poincaré, Note aux C.R. Acad. Sc. Paris, t. 166, 1918, p. 26-28. Zbl46.0522.01JFM46.0522.01
  16. [M-S] MAÑ;É (R.), SAD (P.) et SULLIVAN (D.). — On the dynamics of rational maps, Ann. scient. Éc. norm. sup., 4e série, t. 16, 1983, p. 193-217. Zbl0524.58025MR85j:58089
  17. [N] NEHARI (Z.). — Conformal mappings, Dover Pub., New York, 1975. MR51 #13206
  18. [R] REES (M.). — Ergodic rational maps with dense critical forward orbit, Preprint, Univ. of Minnesota, 1983, à paraître dans Erg. Th. Dyn. syst. Zbl0553.58008
  19. [R1] RÜSSMANN (H.). — Kleine Nenner, II : Bemerkungen zur Newtonschen Methode, Nachr. Akad. Wiss. Göttingen, Math. Phys. Kl, 1972, p. 1-20. Zbl0255.30003MR46 #8407
  20. [R2] RÜSSMANN (H.). — Über die Iteration analytischer Funktionen, J. Math. Mech., vol. 17, 1967, p. 523-532. Zbl0186.47704
  21. [Rd] RUDIN (W.). — Real and complex analysis, McGraw Hill, New York, 1978. Zbl0142.01701
  22. [Sa] SAMUEL (P.). — Théories algébriques des nombres, Hermann, Paris, 1971. 
  23. [Si] SIEGEL (C. L. C.). — Iteration of analytic functions, Ann. Math., vol. 43, 1942, p. 607-612. Zbl0061.14904MR4,76c
  24. [S] SULLIVAN (D.). — Quasi-conformal homeomorphisms and dynamics (I), solution of the Fatou-Julia problem on wandering domains, I.H.E.S., Preprint, 1982, à paraître aux Ann. Math. Zbl0589.30022
  25. [S1] SULLIVAN (D.). — Quasi-conformal homeomorphisms and dynamics (III), topological conjugacy classes of analytic endomorphisms, I.H.E.S., Preprint, 1983. 
  26. [Y1] YOCCOZ (J. C.). — C1-conjugaison des difféomorphismes du cercle, preprint I.M.P.A., Rio de Janeiro, à paraître dans Proc. Symp. Dynamical Systems, Rio de Janeiro, 1981, Springer, Lect. Notes in Math., n° 1007, 1983, p. 815-827. Zbl0537.57015
  27. [Y2] YOCCOZ (J. C.). — Conjugaison différentiable des difféomorphismes du cercle dont le nombre de rotation vérifie une condition diophantienne, preprint I.M.P.A., Rio de Janeiro, 1982, Ann. scient. Ec. norm. sup., 4e série, t. 17, 1984, p. 339-365. Zbl0595.57027
  28. [Z] ZEHNDER (E.). — A simple proof of generalization of a theorem by C. L. Siegel, Lect. Notes in Math., vol. 597, Springer-Verlag, 1977, p. 855-866. Zbl0361.32007MR57 #1560

Citations in EuDML Documents

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  1. Emmanuel Risler, Linéarisation des perturbations holomorphes des rotations et applications
  2. P. Grzegorczyk, F. Przytycki, W. Szlenk, On iterations of Misiurewicz's rational maps on the Riemann sphere
  3. Mitsuhiro Shishikura, On the quasiconformal surgery of rational functions
  4. Feliks Przytycki, Accessibility of typical points for invariant measures of positive Lyapunov exponents for iterations of holomorphic maps
  5. Jean-Benoît Bost, Tores invariants des systèmes dynamiques hamiltoniens
  6. Adrien Douady, Disques de Siegel et anneaux de Herman

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