On the dynamics of polynomial-like mappings

Adrien Douady; John Hamal Hubbard

Annales scientifiques de l'École Normale Supérieure (1985)

  • Volume: 18, Issue: 2, page 287-343
  • ISSN: 0012-9593

How to cite

top

Douady, Adrien, and Hubbard, John Hamal. "On the dynamics of polynomial-like mappings." Annales scientifiques de l'École Normale Supérieure 18.2 (1985): 287-343. <http://eudml.org/doc/82160>.

@article{Douady1985,
author = {Douady, Adrien, Hubbard, John Hamal},
journal = {Annales scientifiques de l'École Normale Supérieure},
keywords = {Mandelbrot set; polynomial-like mapping; quasiconformal map},
language = {eng},
number = {2},
pages = {287-343},
publisher = {Elsevier},
title = {On the dynamics of polynomial-like mappings},
url = {http://eudml.org/doc/82160},
volume = {18},
year = {1985},
}

TY - JOUR
AU - Douady, Adrien
AU - Hubbard, John Hamal
TI - On the dynamics of polynomial-like mappings
JO - Annales scientifiques de l'École Normale Supérieure
PY - 1985
PB - Elsevier
VL - 18
IS - 2
SP - 287
EP - 343
LA - eng
KW - Mandelbrot set; polynomial-like mapping; quasiconformal map
UR - http://eudml.org/doc/82160
ER -

References

top
  1. [A] L. AHLFORS, Lectures on Quasi-Conformal Mappings, Van Nostrand, 1966. Zbl0138.06002MR34 #336
  2. [A-B] L. AHLFORS and L. BERS, The Riemann Mappings Theorem for Variable Metrics (Annals of Math., Vol. 72-2, 1960, pp. 385-404). Zbl0104.29902MR22 #5813
  3. [B-R] L. BERS and ROYDEN, Holomorphic Families of Injections, [Acta Math. (to appear)]. Zbl0619.30027
  4. [Bl] P. BLANCHARD, Complex Analytic Dynamics on the Riemann Sphere, Preprint, M.I.A., Minneapolis, 1983. Bulletin AMS, 1984. 
  5. [Br] H. BROLIN, Invariant Sets Under Iteration of Rational Functions (Arkiv for Math., Vol. 6, 1966, pp. 103-144). Zbl0127.03401MR33 #2805
  6. [C] P. COLLET, Local C∞-Conjugacy on the Julia Set for Some Holomorphic Perturbations of z↦z², preprint, M.I.A., Minneapolis [J. Math. pures et app. (to appear)]. 
  7. [D] A. DOUADY, Systèmes dynamiques holomorphes (Séminaire Bourbaki, 599, November 1982) [Asterisque (to appear)]. Zbl0532.30019
  8. [D-H] A. DOUADY and J. HUBBARD, Itération des polynômes quadratiques complexes (C.R. Acad. Sc., T. 294, série I, 1982, pp. 123-126). Zbl0483.30014MR83m:58046
  9. [E-E] J.-P. ECKMANN and H. EPSTEIN (to appear). 
  10. [E-F] Cl. EARLE and R. FOWLER, Holomorphic Families of Open Riemann Surfaces (to appear). Zbl0537.30036
  11. [F] P. FATOU, Sur les équations fonctionnelles (Bull. Soc. math. Fr., T. 47, 1919, pp. 161-271 ; T. 47, 1920, pp. 33-94 and 208-314). Zbl47.0921.02JFM47.0921.02
  12. [G] R. GODEMENT, Topologie Algébrique et Théorie des Faisceaux, Hermann, Paris, 1958. Zbl0080.16201MR21 #1583
  13. [J] G. JULIA, Mémoires sur l'itération des fonctions rationnelles (J. Math. pures et app., 1918). See also Œuvres Complètes de G. Julia, Gauthier-Villars, Vol. 1, pp. 121-139. JFM46.0520.06
  14. [L-V] O. LEHTO and VIRTAANEN, Quasi-Conformal Mappings in the Plane, Springer Verlag, 1973. Zbl0267.30016
  15. [M] B. MANDELBROT, Fractal Aspects of the Iteration of zˇλz(l - z) (Annals N. Y. Acad. Sc., Vol. 357, 1980, pp. 249-259). Zbl0478.58017
  16. [M-S-S] R. MAÑ;E, P. SAD and D. SULLIVAN, On the Dynamics of Rational Maps [Ann. scient. Ec. Norm. Sup. (to appear)]. Zbl0524.58025
  17. [Ri] S. RICKMAN, Remonability Theorems for Quasiconformal Mappings [Ann. Ac. Scient. Fenn., 449, p. 1-8, (1969)]. Zbl0189.09301MR40 #7443
  18. [R] W. RUDIN, Real and Complex Analysis, McGraw Hill, 1966, 1974. Zbl0142.01701
  19. [S1] D. SULLIVAN, Conformal Dynamical Systems, preprint, I.H.E.S. ; Geometric Dynamics (Springer Lecture Notes). 
  20. [S2] D. SULLIVAN, Quasi-Conformal Homeomorphisms and Dynamics, I, II, III, preprint I.H.E.S. 
  21. [S-T] D. SULLIVAN and W. THURSTON, Holomorphically Moving Sets, preprint I.H.E.S., 1982. 

Citations in EuDML Documents

top
  1. Lluís Alsedà, Núria Fagella, Dynamics on Hubbard trees
  2. Jeremy Kahn, Mikhail Lyubich, A priori bounds for some infinitely renormalizable quadratics: II. Decorations
  3. Karsten Keller, A note on the structure of quadratic Julia sets
  4. Xavier Buff, Ensembles de Julia de mesure positive
  5. I. Popovici, Alexander Volberg, Rigidity of harmonic measure
  6. Lei Tan, Branched coverings and cubic Newton maps
  7. Sebastian van Strien, Misiurewicz maps unfold generically (even if they are critically non-finite)
  8. Mikhail Lyubich, Michael Yampolsky, Dynamics of quadratic polynomials : complex bounds for real maps
  9. Jacek Graczyk, Grzegorz Świątek, Induced expansion for quadratic polynomials
  10. Alexis Marin, Géométrie des polynômes. Coût global moyen de la méthode de Newton

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.