Linéarisation des perturbations holomorphes des rotations et applications
Mémoires de la Société Mathématique de France (1999)
- Volume: 77, page III1-VII102
- ISSN: 0249-633X
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topRisler, Emmanuel. "Linéarisation des perturbations holomorphes des rotations et applications." Mémoires de la Société Mathématique de France 77 (1999): III1-VII102. <http://eudml.org/doc/94928>.
@article{Risler1999,
author = {Risler, Emmanuel},
journal = {Mémoires de la Société Mathématique de France},
keywords = {holomorphic dynamical system; rotation number; small divisor; Brjuno condition; Stein manifold; local linearization; Whitney regularity; Siegel disk; Herman ring; analytic circle diffeomorphisms; -bar problem; holomorphic map},
language = {fre},
pages = {III1-VII102},
publisher = {Société mathématique de France},
title = {Linéarisation des perturbations holomorphes des rotations et applications},
url = {http://eudml.org/doc/94928},
volume = {77},
year = {1999},
}
TY - JOUR
AU - Risler, Emmanuel
TI - Linéarisation des perturbations holomorphes des rotations et applications
JO - Mémoires de la Société Mathématique de France
PY - 1999
PB - Société mathématique de France
VL - 77
SP - III1
EP - VII102
LA - fre
KW - holomorphic dynamical system; rotation number; small divisor; Brjuno condition; Stein manifold; local linearization; Whitney regularity; Siegel disk; Herman ring; analytic circle diffeomorphisms; -bar problem; holomorphic map
UR - http://eudml.org/doc/94928
ER -
References
top- [1] L. V. Ahlfors, L. Bers, Riemann's mapping theorem for variable metrics, Ann. of Math., 72 (1960), 385-404. Zbl0104.29902MR22 #5813
- [2] V. I. Arnold, On the mappings of the circumference onto itself, Translations A.M.S., vol. 46, 2nd series (1965), 213-284. Zbl0152.41905
- [3] V. I. Arnold, Geometrical methods in the theory of ordinary differential equations, Grundlehren der mathematischen Wissenschaften 250, Springer-Verlag (1983). Zbl0507.34003MR84d:58023
- [4] A. D. Bruno, Analytical form of differential equations, Transactions Moscow Math. Soc. 25 (1971), 131-288 ; 26 (1972), 199-239. Zbl0272.34018
- [5] L. Carleson, T. W. Gamelin, Complex dynamics, Springer-Verlag (1991). Zbl0782.30022
- [6] M. R. Herman, Exemples de fractions rationnelles ayant une orbite dense sur la sphère de Riemann, Bull. Soc. Math. France, 112 (1984), 93-142. Zbl0559.58020MR86d:58055
- [7] M. R. Herman, Simple proofs of local conjugacy theorems of diffeomorphisms of the circle with almost every rotation number, Bol. Soc. Bras. Mat. 16, 1 (1985), 45-53. Zbl0651.58008MR87f:58085
- [8] L. Hörmander, An introduction to complex analysis in several variables, North Holland Mathematical Library, 2ème édition, (1973). Zbl0271.32001
- [9] J. H. Hubbard, Sur les sections analytiques de la courbe universelle de Teichmüller, Memoirs of the A.M.S., vol. 4, No 166 (1976). Zbl0318.32020MR55 #3326
- [10] S. Lang, Introduction to diophantine approximation, Addison Wesley, New York (1966). Zbl0144.04005MR35 #129
- [11] R. Mañ;e, On the instability of Herman rings, Inv. Math. 81 (1985), 459-471. Zbl0595.30032MR87e:58119
- [12] R. Pérez-Marco, J.-C. Yoccoz, Germes de feuilletages holomorphes à holonomie prescrite, Astérisque 222, (1994), 345-371. Zbl0809.32008MR96b:58090
- [13] E. Risler, Dynamique des perturbations holomorphes des rotations, Thèse de l'École Polytechnique (1996).
- [14] H. Rüssmann, Kleine Nenner II: Bemerkungen zur Newtonschen Methode, Nachr. Akad. Wiss. Göttingen, Math. Phys. K1 (1972), 1-20. Zbl0255.30003MR46 #8407
- [15] H. Rüssmann, On the frequencies of quasi-periodic solutions of analytic nearly integrable Hamiltonian systems, Seminar on Dynamical Systems (St Pet. 91), S. Kuksin, V. Lazutkin, J. Pöschel eds., Progress in Nonlinear Differential Equations and their Applications, Birkhäuser (1994). Zbl0797.58028
- [16] C. L. Siegel, Iteration of analytic functions, Ann. of Math., 43 (1942), 807-812. Zbl0061.14904MR4,76c
- [17] H. Whitney, Analytic extensions of differentiable functions defined in closed sets, Trans. Amer. Math. Soc. 36 (1934), 63-89. Zbl0008.24902MR1501735JFM60.0217.01
- [18] J.-C. Yoccoz, Théorème de Siegel, nombres de Bruno et polynôme quadratique, Astérisque 231 (1995), 3-88. MR96m:58214
- [19] J.-C. Yoccoz, Conjugaison des difféomorphismes analytiques du cercle, manuscrit (1988).
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