Systèmes dynamiques holomorphes

Adrien Douady

Séminaire Bourbaki (1982-1983)

  • Volume: 25, page 39-63
  • ISSN: 0303-1179

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Douady, Adrien. "Systèmes dynamiques holomorphes." Séminaire Bourbaki 25 (1982-1983): 39-63. <http://eudml.org/doc/110016>.

@article{Douady1982-1983,
author = {Douady, Adrien},
journal = {Séminaire Bourbaki},
keywords = {rational map; Julia set; Mandelbrot set; Hubbard trees; coupling of polynomials; modulation of polynomials},
language = {fre},
pages = {39-63},
publisher = {Société Mathématique de France},
title = {Systèmes dynamiques holomorphes},
url = {http://eudml.org/doc/110016},
volume = {25},
year = {1982-1983},
}

TY - JOUR
AU - Douady, Adrien
TI - Systèmes dynamiques holomorphes
JO - Séminaire Bourbaki
PY - 1982-1983
PB - Société Mathématique de France
VL - 25
SP - 39
EP - 63
LA - fre
KW - rational map; Julia set; Mandelbrot set; Hubbard trees; coupling of polynomials; modulation of polynomials
UR - http://eudml.org/doc/110016
ER -

References

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  1. [Bn] A.D. Brjuno - Analytical form of differential equations, Trans. Moscow Math. Soc., 25(1971), 131-288. Zbl0272.34018MR377192
  2. [Br] M. Brolin - Invariant sets under iteration of rational functions, Arkiv for Mathematik6(1966), 103-144. Zbl0127.03401MR194595
  3. [F] P. Fatou - Mémoire sur les équations fonctionnelles, B.S.M.F.47(1919), 161- 271, 47(1920), 33-94 et 208-314. Zbl47.0921.02MR1504787JFM47.0921.02
  4. [J] G. Julia - Itération des applications fonctionnelles, J. Math. Pures et Appl. (1918), 47-245. JFM46.0520.06
  5. [L] S. Lattès - Sur l'itération des substitutions rationnelles et les fonctions de Poincaré, C.R.A.S.166(1918), 26-28. JFM46.0522.01
  6. [Rm] H. Rüssmann - Kleine Nenner II : Bemerkungen zur Newton'schen Methode, Math. Phys. K1. (1972), 1-20. Zbl0255.30003MR309297
  7. [Si] C.L.C. Siegel - Iteration of analytic functions, Ann. Math.43(1942), 607-612. Zbl0061.14904MR7044
  8. [Z] E. Zehnder - A simple proof of a generalisation of a theorem by Siegel, Springer-Verlag, Lect. Notes in Maths.597(1977), 855-866. Zbl0361.32007MR461575
  9. [Bo] R. Bowen - Dimension of quasi-circles, Publ. I.H.E.S., Vol. 50(1980). 
  10. [DH] A. Douady et J.H. Hubbard - Itération des polynômes quadratiques complexes, C.R.A.S., t. 294 (18 janvier 1982). Zbl0483.30014MR651802
  11. [Fe] M.J. Feigenbaum - Quantitative universality for a class of non-linear transformations, J. Stat. Phys. 19-1(1978), 25-52. Zbl0509.58037MR501179
  12. [H] M. Herman - Exemples de fractions rationnelles ayant une orbite dense sur la sphère de Riemann, (manuscrit). Zbl0559.58020
  13. [Lf] O.E. Lanford - Smooth transformations of intervals, Sém. Bourbaki, exposé n° 563, Springer-Verlag, Lect. Notes in Maths.901(1981), 36-54. Zbl0514.58028MR647487
  14. [M1] B. Mandelbrot - Fractal aspects of the iteration of z ↦ λz (1 - z) for complex λ and z , Annals N.Y. Acad. of Sc.357(1980), 249-259. Zbl0478.58017
  15. [M2] B. Mandelbrot - The Fractal Geometry of Nature, Freeman edit., San Francisco. Zbl0504.28001MR665254
  16. [Mt] J. Martinet - Normalisation des champs de vecteurs holomorphes (d'après A.D. Brjuno), Sém. Bourbaki, exposé n° 564, Springer-Verlag, Lect. Notes in Maths.901(1981), 55-70. Zbl0481.34013MR647488
  17. [MSS] R. Mañe, P. Sad and D. Sullivan - On the Dynamics of rational maps, à paraître aux Annales de l'E.N.S.. Zbl0524.58025
  18. [R] D. Ruelle - Analytic repellers, J. of Ergodic Theory and Dynamical Systems, 1982. MR684247
  19. [S1] D. Sullivan - Density at infinity, Publ. I.H.E.S., Vol. 50(1980). 
  20. [S2] D. Sullivan - Conformal Dynamical Systems, preprint, I.H.E.S.. MR730296
  21. [S3] D. Sullivan - Quasi-conformal homeomorphisms and Dynamics I, II et III, preprints I.H.E.S., soumis aux Annals of Maths. en 1982. MR634434
  22. [ST] D. Sullivan and W. Thurston - Note on structural stability of rational maps, preprint I.H.E.S., 1982. 
  23. [DH2] A. Douady et J.H. Hubbard- Dynamique des applications à allure polynômiale, preprint I.R.M.A.Strasbourg, 1983. 
  24. [M∞] B. MandelbrotLes fractals, les monstres et la beauté, Le Débat n° 24, mars 1983 (Gallimard Ed.). 
  25. [MN] N.S. Manton and M. Nauenberg- Universal scaling behavior for itered maps in the complex plane, Comm. in Math. Phys. (1983). Zbl0523.30018MR713685

Citations in EuDML Documents

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  1. Robert L. Devaney, Linda Keen, Dynamics of meromorphic maps : maps with polynomial schwarzian derivative
  2. Pascale Roesch, Introduction
  3. A. Douady, J. H. Hubbard, Dynamique des applications à allure polynomiale
  4. Lei Tan, Branched coverings and cubic Newton maps
  5. Pierre Moussa, Itération des polynômes et propriétés d'orthogonalité
  6. Lisa R. Goldberg, John Milnor, Fixed points of polynomial maps. Part II. Fixed point portraits
  7. Adrien Douady, John Hamal Hubbard, On the dynamics of polynomial-like mappings
  8. Guizhen Cui, Wenjuan Peng, Lei Tan, On a theorem of Rees-Shishikura
  9. P. Moussa, Un opérateur de Schrödinger presque périodique à spectre singulier associé aux itérations d'un polynôme
  10. G. Levin, On Pommerenke's inequality for the eigenvalues of fixed points

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