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. 
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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.. https://www.numdam.org/item/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