Disques de Siegel et anneaux de Herman
Séminaire Bourbaki : volume 1986/87, exposés 669-685, Astérisque, no. 152-153 (1987), Exposé no. 677, 22 p.

Voir la notice du chapitre de livre provenant de la source Numdam

MR Zbl
Douady, Adrien. Disques de Siegel et anneaux de Herman, dans Séminaire Bourbaki : volume 1986/87, exposés 669-685, Astérisque, no. 152-153 (1987), Exposé no. 677, 22 p.. http://geodesic.mathdoc.fr/item/SB_1986-1987__29__151_0/
@incollection{SB_1986-1987__29__151_0,
     author = {Douady, Adrien},
     title = {Disques de {Siegel} et anneaux de {Herman}},
     booktitle = {S\'eminaire Bourbaki : volume 1986/87, expos\'es 669-685},
     series = {Ast\'erisque},
     note = {talk:677},
     pages = {151--172},
     year = {1987},
     publisher = {Soci\'et\'e math\'ematique de France},
     number = {152-153},
     mrnumber = {936853},
     zbl = {0638.58023},
     language = {fr},
     url = {http://geodesic.mathdoc.fr/item/SB_1986-1987__29__151_0/}
}
TY  - CHAP
AU  - Douady, Adrien
TI  - Disques de Siegel et anneaux de Herman
BT  - Séminaire Bourbaki : volume 1986/87, exposés 669-685
AU  - Collectif
T3  - Astérisque
N1  - talk:677
PY  - 1987
SP  - 151
EP  - 172
IS  - 152-153
PB  - Société mathématique de France
UR  - http://geodesic.mathdoc.fr/item/SB_1986-1987__29__151_0/
LA  - fr
ID  - SB_1986-1987__29__151_0
ER  - 
%0 Book Section
%A Douady, Adrien
%T Disques de Siegel et anneaux de Herman
%B Séminaire Bourbaki : volume 1986/87, exposés 669-685
%A Collectif
%S Astérisque
%Z talk:677
%D 1987
%P 151-172
%N 152-153
%I Société mathématique de France
%U http://geodesic.mathdoc.fr/item/SB_1986-1987__29__151_0/
%G fr
%F SB_1986-1987__29__151_0

[A-B] L. V. Ahlfors and L. Bers - Riemann's mapping theorem for variable metrics, Ann. of Math. 72 (1960), 385-404. | Zbl | MR

[A-Beu] L. V. Ahlfors and A. Beurling - The boundary correspondence under quasi-conformal mappings, Acta Math. 96 (1956) , 125-142. | Zbl | MR

[Ar] V. I. Arnold - Small denominators I ; on the mappings of a circumference onto itself, Amer. Math. Soc. Translations, 2nd series, 46 (1961), 213-284. | Zbl

[Bl] P. Blanchard - Complex analytic dynamics on the Riemann sphere, Bull. Amer. Math. Soc. 11 (1984), 85-141. | Zbl | MR

[Brjul] A. D. Brjuno - Convergence of trans formations of differential equations to normal forms, Dokl. Akad. Nauk. URSS 165 (1965), 987-989. | Zbl | MR

[Brju2] A. D. Brjuno - Analytic form of differential equations, Transactions Moscow Math. Soc. 25 (1971), 131-288 ; 26 (1972), 199-239. | Zbl | MR

[Bro] H. Brolin - Invariant sets under iteration of rational functions, Ark Math. 6 (1966), 103-144. | Zbl | MR

[Ca] C. Camacho - On the local structure of conformal mappings and holomorphic vector fields, Astérisque 59-60 (1978) , 83-84. | Zbl | MR | Numdam

[C-J] L. Carleson and P. Jones - Lettre à Herman, 1984.

[Crl] H. Cremer - Über die Iteration rationaler Funktionen, Jahresber, Deutsch. Math. Verein 33 (1925), 185-210. | JFM

[Cr2] H. Cremer - Zum Zentrumproblem, Math. Ann. 98 (1928), 151-163. | MR | JFM

[Cr3] H. Cremer - Über Konvergenz und Zentrumproblem, Math. Ann. 110 (1935), 739-744. | MR | JFM

[Cr4] H. Cremer - Über die Häufigkeit der Nichtzentren, ibid. 115 (1938), 573- 580. | MR | JFM

[D1] A. Douady - Systèmes dynamiques holomorphes, Sém. Bourbaki, exp. 599, Astérisque 105-106 (1983), 39-63. | Zbl | MR | Numdam

[D2] A. Douady - Chirurgie sur les applications holomorphes, ICM 86, Berkeley. Version anglaise : preprint MSRI, 1986. | Zbl | MR

[DH1] A. Douady et J. H. Hubbard - Itération des polynômes quadratiques complexes, C.R. Acad. Sc. Paris, t. 294 (18 Janvier 1982), Série 1, 123-126. | Zbl | MR

[DH2] A. Douady et J. H. Hubbard - Systèmes dynamiques holomorphes I, II : Itération des polynômes complexes (Cours 83-84), Publ. Math. Orsay, 84.02 et 85.04.

[DH3] A. Douady and J. H. Hubbard - On the dynamics of polynomial like mappings, Ann. Sc. E.N.S., 4ème série, 18 (1985), 287-343. | Zbl | MR | Numdam

[D-E] A. Douady and C. Earle - Conformally natural extension of homeomorphisms of the circle, Acta Math., Vol. 157 (1986) 23-48. | Zbl | MR

[F] P. Fatou - Sur les équations fonctionnelles, Bull. S.M.F. 47 (1919), 161- 271 (1920), 33-94 ; 48 (1920), 208-304. | MR | JFM | Numdam

[G] E. Ghys - Transformations holomorphes au voisinage d'une courbe de Jordan, C.R. Acad. Sc. Paris, t. 289 (1984), 385-388. | Zbl | MR

[Gu] J. Guckenheimer - Endomorphisms of the Riemann sphere, Proceedings of the Symposium of Pure Mathematics, v. 14, edited by S. Chern and S. Smale, AMS, Providence, R.I. (1970), 95-123. | Zbl | MR

[H1] M. Herman - Sur la conjugaison différentiable des difféomorphismes du cercle à des rotations, Publ. Math. IHES 49 (1979), 5-233. | Zbl | MR | Numdam

[H2] M. Herman - Exemples de fractions rationnelles ayant une orbite dense sur la sphere de Riemann, Bull. S.M.F. 112 (1984) , 93-142. | Zbl | MR | Numdam

[H3] M. R. Herman - Construction of some curious diffeomorphisms of the Riemann sphere, to appear in J. London Math. Soc. | Zbl | MR

[H4] M. R. Herman - Simple proofs of local conjugacy theorems for diffeomorphisms of the circle with almost every rotation number, Bol. Soc. Bras. Mat. 16 (1985), 45-83. | Zbl | MR

[H5] M. R. Herman - Are the critical points on the boundaries of singular domains ?, Comm. Math. Phys. 99 (1985), 593-612. | Zbl | MR

[H6] M. Herman - Conjugaison quasi-symétrique des difféomorphismes du cercle et applications aux disques singuliers de Siegel, manuscrit (1986).

[H7] M. R. Herman - Recent results and some open questions on Siegel linearization theorem of germs of complex-analytic diffeomorphisms of Cn near a fixed point, 8th International Congress on Mathematical Physics, World Scientific Publishers, 1986.

[Il] Y. S. Il'Yashenko - Divergence of series reducing an analytic differential equation to linear normal form at a singular point, Funct. Analysis and Appl. 13 (1979), 227-229. | Zbl | MR

[J] G. Julia - Oeuvres, vol. I, Gauthier-Villars, Paris.

[L-V] O. Lehto and K. I. Virtanen - Quasiconformal mappings in the plane, Springer-Verlag, 1973. | Zbl | MR

[Lju] M. Ljubich - The investigation of the stability of rational functions, in Theory of Functions, Kharkov (1981), 42, 72-91 (en russe). | Zbl

[M-S-S] R. Mañé, P. Sad and D. Sullivan - On the dynamics of rational maps, Ann. Scient. Ec. Norm. Sup., 4e Série, t. 16 (1982), 193-217. | Zbl | MR | Numdam

[M-N] N. S. Manton and M. Nauenberg - Universal scaling behavior for iterated maps in the complex plane, Comm. in Mathematical Physics ? | Zbl

[Mar] J. Martinet - Normalisation des champs de vecteurs, d'après A.D. Brjuno, Sém. Bourbaki, exp. 564, Lect. Notes in Math., Springer-Verlag 901 (1981), 55-70. | Zbl | MR | Numdam

[Mo] J. Moser - A rapidly convergent iteration method, II, Ann. Scuola Norm. Sup. di Pisa, Ser. III, 20 (1966), 499-535. | Zbl | MR | Numdam

[N] V. I. Naïshul - Topological invariants of analytic and area-preserving mappings and their applications to analytic differential equations in C2 and CP2, Trans. Moscow Math. Soc. 42 (1983), 239-250. | Zbl

[P] J. Pöschel - On invariant manifolds of complex analytic mappings near fixed points, Exp. Math. 4 (1986), 97-109 ; Addendum p. 1 to 4. | MR

[Rel] M. Rees - Ergodic rational maps with dense critical point forward orbit, University of Minnesota Math. Report, 82-140.

[Re2] M. Rees - Positive measure sets of ergodic rational maps, Ann. Sc. E.N.S., t. 19, fasc. 3 (1986), 383-407. | Zbl | MR | Numdam

[R1] H. Rüssmann - Über die Iteration analytischer Funktionen, J. Math. Mech. 17 ( 1967) , 523-532. | Zbl | MR

[R2] H. Rüssmann - Kleine Nenne, II : Bemerkungen zur Newtonschen Methode, Nachr. Akad. Wiss. Göttingen, Math. Phys. Kl. (1970), 1-10. | Zbl | MR

[R3] H. Rüssmann - On the convergence of power series transformations of analytic mapping near a fixed point into normal form, preprint, I.H.E.S. (1977).

[Sch] W. M. Schmidt - Diophantine approximation, Lect. Notes in Math., Springer-Verlag 785 (1980). | Zbl | MR

[Sh1] M. Shishikura - On the quasi-conformal surgery of rational functions, Ann. Sc. E.N.S., t. 20, fasc. 1 (1987). | Zbl | MR | Numdam

[Sh2] M. Shishikura - Configurations of Herman rings and dynamical systems on trees, preprint, Kyoto University (1986).

[Sie] C. L. Siegel - Iteration of analytic functions, Ann. Math. 43 (1942), 807- 812 (voir aussi Siegel, Oeuvres, Springer-Verlag (1966)). | Zbl | MR

[Sul] D. Sullivan - Quasi-conformal homeomorphisms, I, Solutions of the Fatou-Julia problem on wandering domains, Annals of Math. 122 (1985), 401-418. | Zbl | MR

[Su2] D. Sullivan - Quasi-conformal homeomorphisms and dynamics, II, III : topological conjugacy classes of analytic endomorphisms, preprint IHES (1983). | MR

[Su-T] D. Sullivan and W. Thurston - Extending holomorphic motions, preprint. | MR

[Y1] J.-C. Yoccoz - Conjugaison différentiable des difféomorphismes du cercle dont le nombre de rotation vérifie une condition diophantienne, Ann. Sc. E.N.S., 4ème série, 17 (1984), 333-359. | Zbl | MR | Numdam

[Y2] J.-C. Yoccoz - C1-conjugaison des difféomorphismes du cercle, Lect. Notes in Math., Springer-Verlag, 1007 (1983), 814-827. | Zbl | MR

[Y3] J.-C. Yocooz Il n'y a pas de contre-exemple de Denjoy analytique, Note C.R.A.S., t. 298, Série I, n° 7 (1984), 141-144. | Zbl | MR

[Y4] J.-C. Yoccoz - Théorème de Siegel pour les polynômes quadratiques, manuscrit (1985).

[Y5] J.-C. Yoccoz - Centralisateur et conjugaison différentiable des difféomorphismes du cercle, Thèse Université de Paris-Sud (contient [Y1] et [Y3]).

[Y6] J.-C. Yoccoz - Une remarque sur la condition de Brjuno, manuscrit (1985).

[Z1] E. Zehnder - A simple proof of a generalization of a theorem by C. L. Siegel, Lect. Notes in Math., Springer-Verlag 597 (1977), 855-866. | Zbl | MR

[Z2] E. Zehnder - Generalized implicit function theorems with applications to some small divisor problems, I, Comm. Pure Appl. Math. 28 (1975), 91-140 ; II, ibid. 29 (1976), 49-111. | Zbl | MR