Linéarisation des perturbations holomorphes des rotations et applications

Emmanuel Risler

Mémoires de la Société Mathématique de France (1999)

  • Volume: 77, page III1-VII102
  • ISSN: 0249-633X

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Risler, 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

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  2. [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. [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. [4] A. D. Bruno, Analytical form of differential equations, Transactions Moscow Math. Soc. 25 (1971), 131-288 ; 26 (1972), 199-239. Zbl0272.34018
  5. [5] L. Carleson, T. W. Gamelin, Complex dynamics, Springer-Verlag (1991). Zbl0782.30022
  6. [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. [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
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  10. [10] S. Lang, Introduction to diophantine approximation, Addison Wesley, New York (1966). Zbl0144.04005MR35 #129
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  12. [12] R. Pérez-Marco, J.-C. Yoccoz, Germes de feuilletages holomorphes à holonomie prescrite, Astérisque 222, (1994), 345-371. Zbl0809.32008MR96b:58090
  13. [13] E. Risler, Dynamique des perturbations holomorphes des rotations, Thèse de l'École Polytechnique (1996). 
  14. [14] H. Rüssmann, Kleine Nenner II: Bemerkungen zur Newtonschen Methode, Nachr. Akad. Wiss. Göttingen, Math. Phys. K1 (1972), 1-20. Zbl0255.30003MR46 #8407
  15. [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. [16] C. L. Siegel, Iteration of analytic functions, Ann. of Math., 43 (1942), 807-812. Zbl0061.14904MR4,76c
  17. [17] H. Whitney, Analytic extensions of differentiable functions defined in closed sets, Trans. Amer. Math. Soc. 36 (1934), 63-89. Zbl0008.24902MR1501735JFM60.0217.01
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  19. [19] J.-C. Yoccoz, Conjugaison des difféomorphismes analytiques du cercle, manuscrit (1988). 

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