Disques de Siegel et anneaux de Herman

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1. [A-B] L.V. Ahlfors and L. Bers - Riemann's mapping theorem for variable metrics, Ann. of Math.72 (1960), 385-404. Zbl0104.29902MR115006
2. [A-Beu] L.V. Ahlfors and A. Beurling - The boundary correspondence under quasi-conformal mappings, Acta Math.96 (1956) , 125-142. Zbl0072.29602MR86869
3. [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. Zbl0152.41905
4. [Bl] P. Blanchard - Complex analytic dynamics on the Riemann sphere, Bull. Amer. Math. Soc.11 (1984), 85-141. Zbl0558.58017MR741725
5. [Brjul] A.D. Brjuno - Convergence of trans formations of differential equations to normal forms, Dokl. Akad. Nauk. URSS165 (1965), 987-989. Zbl0146.11301MR192098
6. [Brju2] A.D. Brjuno - Analytic form of differential equations, Transactions Moscow Math. Soc.25 (1971), 131-288 ; 26 (1972), 199-239. Zbl0283.34013MR377192
7. [Bro] H. Brolin - Invariant sets under iteration of rational functions, Ark Math.6 (1966), 103-144. Zbl0127.03401MR194595
8. [Ca] C. Camacho - On the local structure of conformal mappings and holomorphic vector fields, Astérisque59-60 (1978) , 83-84. Zbl0415.30015MR542732
9. [C-J] L. Carleson and P. Jones - Lettre à Herman, 1984. 
10. [Crl] H. Cremer - Über die Iteration rationaler Funktionen, Jahresber, Deutsch. Math. Verein33 (1925), 185-210. Zbl51.0262.05JFM51.0262.05
11. [Cr2] H. Cremer - Zum Zentrumproblem, Math. Ann.98 (1928), 151-163. MR1512397JFM53.0303.04
12. [Cr3] H. Cremer - Über Konvergenz und Zentrumproblem, Math. Ann.110 (1935), 739-744. Zbl0010.30704MR1512966JFM61.0328.04
13. [Cr4] H. Cremer - Über die Häufigkeit der Nichtzentren, ibid. 115 (1938), 573- 580. Zbl0018.36802MR1513203JFM64.0289.02
14. [D1] A. Douady - Systèmes dynamiques holomorphes, Sém. Bourbaki, exp. 599, Astérisque105-106 (1983), 39-63. Zbl0532.30019MR728980
15. [D2] A. Douady - Chirurgie sur les applications holomorphes, ICM86, Berkeley. Version anglaise : preprint MSRI, 1986. Zbl0698.58048MR934275
16. [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. Zbl0483.30014MR651802
17. [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. 
18. [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. Zbl0587.30028MR816367
19. [D-E] A. Douady and C. Earle - Conformally natural extension of homeomorphisms of the circle, Acta Math., Vol. 157 (1986) 23-48. Zbl0615.30005MR857678
20. [F] P. Fatou - Sur les équations fonctionnelles, Bull. S.M.F.47 (1919), 161- 271 (1920), 33-94 ; 48 (1920), 208-304. Zbl47.0921.02MR1504792JFM47.0921.02
21. [G] E. Ghys - Transformations holomorphes au voisinage d'une courbe de Jordan, C.R. Acad. Sc. Paris, t. 289 (1984), 385-388. Zbl0573.58021MR748928
22. [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. Zbl0205.54102MR274740
23. [H1] M. Herman - Sur la conjugaison différentiable des difféomorphismes du cercle à des rotations, Publ. Math. IHES49 (1979), 5-233. Zbl0448.58019MR538680
24. [H2] M. Herman - Exemples de fractions rationnelles ayant une orbite dense sur la sphere de Riemann, Bull. S.M.F.112 (1984) , 93-142. Zbl0559.58020MR771920
25. [H3] M.R. Herman - Construction of some curious diffeomorphisms of the Riemann sphere, to appear in J. London Math. Soc. Zbl0603.58017MR856520
26. [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. Zbl0651.58008MR819805
27. [H5] M.R. Herman - Are the critical points on the boundaries of singular domains ?, Comm. Math. Phys.99 (1985), 593-612. Zbl0587.30040MR796014
28. [H6] M. Herman - Conjugaison quasi-symétrique des difféomorphismes du cercle et applications aux disques singuliers de Siegel, manuscrit (1986). 
29. [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. 
30. [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. Zbl0477.34004MR545377
31. [J] G. Julia - Oeuvres, vol. I, Gauthier-Villars, Paris. 
32. [L-V] O. Lehto and K.I. Virtanen - Quasiconformal mappings in the plane, Springer-Verlag, 1973. Zbl0267.30016MR344463
33. [Lju] M. Ljubich - The investigation of the stability of rational functions, in Theory of Functions, Kharkov (1981), 42, 72-91 (en russe). Zbl0572.30023
34. [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. Zbl0524.58025MR732343
35. [M-N] N.S. Manton and M. Nauenberg - Universal scaling behavior for iterated maps in the complex plane, Comm. in Mathematical Physics ? Zbl0523.30018
36. [Mar] J. Martinet - Normalisation des champs de vecteurs, d'après A.D. Brjuno, Sém. Bourbaki, exp. 564, Lect. Notes in Math., Springer-Verlag901 (1981), 55-70. Zbl0481.34013MR647488
37. [Mo] J. Moser - A rapidly convergent iteration method, II, Ann. Scuola Norm. Sup. di Pisa, Ser. III, 20 (1966), 499-535. Zbl0144.18202MR206461
38. [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. Zbl0527.58035
39. [P] J. Pöschel - On invariant manifolds of complex analytic mappings near fixed points, Exp. Math.4 (1986), 97-109 ; Addendum p. 1 to 4. MR879908
40. [Rel] M. Rees - Ergodic rational maps with dense critical point forward orbit, University of Minnesota Math. Report, 82-140. 
41. [Re2] M. Rees - Positive measure sets of ergodic rational maps, Ann. Sc. E.N.S., t. 19, fasc. 3 (1986), 383-407. Zbl0611.58038MR870689
42. [R1] H. Rüssmann - Über die Iteration analytischer Funktionen, J. Math. Mech.17 ( 1967) , 523-532. Zbl0186.47704MR218535
43. [R2] H. Rüssmann - Kleine Nenne, II : Bemerkungen zur Newtonschen Methode, Nachr. Akad. Wiss. Göttingen, Math. Phys. Kl. (1970), 1-10. Zbl0255.30003MR309297
44. [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). 
45. [Sch] W.M. Schmidt - Diophantine approximation, Lect. Notes in Math., Springer-Verlag785 (1980). Zbl0421.10019MR568710
46. [Sh1] M. Shishikura - On the quasi-conformal surgery of rational functions, Ann. Sc. E.N.S., t. 20, fasc. 1 (1987). Zbl0621.58030MR892140
47. [Sh2] M. Shishikura - Configurations of Herman rings and dynamical systems on trees, preprint, Kyoto University (1986). 
48. [Sie] C.L. Siegel - Iteration of analytic functions, Ann. Math.43 (1942), 807- 812 (voir aussi Siegel, Oeuvres, Springer-Verlag (1966)). Zbl0061.14904MR7044
49. [Sul] D. Sullivan - Quasi-conformal homeomorphisms, I, Solutions of the Fatou-Julia problem on wandering domains, Annals of Math.122 (1985), 401-418. Zbl0589.30022MR819553
50. [Su2] D. Sullivan - Quasi-conformal homeomorphisms and dynamics, II, III : topological conjugacy classes of analytic endomorphisms, preprint IHES (1983). MR730296
51. [Su-T] D. Sullivan and W. Thurston - Extending holomorphic motions, preprint. MR857674
52. [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. Zbl0595.57027MR777374
53. [Y2] J.-C. Yoccoz - C1-conjugaison des difféomorphismes du cercle, Lect. Notes in Math., Springer-Verlag, 1007 (1983), 814-827. Zbl0537.57015MR730301
54. [Y3] J.-C. YocoozIl n'y a pas de contre-exemple de Denjoy analytique, Note C.R.A.S., t. 298, Série I, n° 7 (1984), 141-144. Zbl0573.58023MR741080
55. [Y4] J.-C. Yoccoz - Théorème de Siegel pour les polynômes quadratiques, manuscrit (1985). 
56. [Y5] J.-C. Yoccoz - Centralisateur et conjugaison différentiable des difféomorphismes du cercle, Thèse Université de Paris-Sud (contient [Y1] et [Y3]). 
57. [Y6] J.-C. Yoccoz - Une remarque sur la condition de Brjuno, manuscrit (1985). 
58. [Z1] E. Zehnder - A simple proof of a generalization of a theorem by C. L. Siegel, Lect. Notes in Math., Springer-Verlag597 (1977), 855-866. Zbl0361.32007MR461575
59. [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. Zbl0309.58006MR380867

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