The nilpotent part and distinguished form of resonant vector fields or diffeomorphisms

J. Ecalle; D. Schlomiuk

Annales de l'institut Fourier (1993)

  • Volume: 43, Issue: 5, page 1407-1483
  • ISSN: 0373-0956

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Ecalle, J., and Schlomiuk, D.. "The nilpotent part and distinguished form of resonant vector fields or diffeomorphisms." Annales de l'institut Fourier 43.5 (1993): 1407-1483. <http://eudml.org/doc/75043>.

@article{Ecalle1993,
author = {Ecalle, J., Schlomiuk, D.},
journal = {Annales de l'institut Fourier},
keywords = {singularities; normal forms; resurgent functions},
language = {eng},
number = {5},
pages = {1407-1483},
publisher = {Association des Annales de l'Institut Fourier},
title = {The nilpotent part and distinguished form of resonant vector fields or diffeomorphisms},
url = {http://eudml.org/doc/75043},
volume = {43},
year = {1993},
}

TY - JOUR
AU - Ecalle, J.
AU - Schlomiuk, D.
TI - The nilpotent part and distinguished form of resonant vector fields or diffeomorphisms
JO - Annales de l'institut Fourier
PY - 1993
PB - Association des Annales de l'Institut Fourier
VL - 43
IS - 5
SP - 1407
EP - 1483
LA - eng
KW - singularities; normal forms; resurgent functions
UR - http://eudml.org/doc/75043
ER -

References

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  1. [B] A.D. BRYUNO (often transliterated as BRUNO or BRJUNO), Analytical forms of differential equations I, II, Trudy Mosk. Mat. Ob., 25 (1971), 119-262; 26 (1972), 199-239; English translation in Trans. Mosc. Math. Soc., 25 (1971), 26 (1972). Zbl0283.34013
  2. [E1] J. ECALLE, Les fonctions résurgentes, vol. 1, Algèbres de fonctions résurgentes, Publ. Math. Orsay, 1981. Zbl0499.30034
  3. [E2] J. ECALLE, Les fonctions résurgentes, vol. 2, Les fonctions résurgentes appliquées à l'itération, Publ. Math. Orsay, 1981. Zbl0499.30034
  4. [E3] J. ECALLE, Les fonctions résurgentes, vol. 3, L'équation du pont et la classification analytique des objets locaux, Publ. Math. Orsay, 1985. Zbl0602.30029
  5. [E4] J. ECALLE, Finitude des cycles-limites et accéléro-sommation de l'application de retour, in: Bifurcations of Planar Vector Fields (J.-P. Françoise, R. Roussarie, eds). Lecture Notes in Math. 1455, Springer-Verlag, Berlin-Heidelberg-New York (1990), 74-159. Zbl0729.34016MR92e:58166
  6. [E5] J. ECALLE, Introduction aux fonctions analysables et preuve constructive de la conjecture de Dulac, Actualités Math. Hermann, Paris, 1992. 
  7. [E6] J. ECALLE, The bridge equation and its applications to local geometry, Proc. Internat. Conf. Dynam. Syst., Nagoya (Sept. 1990) (K. Shiraiwa, ed.), Adv. Ser. Dynam. Syst., 9. 
  8. [E7] J. ECALLE, Singularités non abordables par la géométrie, Ann. Inst. Fourier (Grenoble), 42 (1-2) (1992), 73-164. Zbl0940.32013MR93f:58214
  9. [E8] J. ECALLE, Compensation of small denominators and ramified linearization of local objects, Prepubl. Math. Orsay (1992), n° 92-53; to appear in Astérisque, Proc. Conf. Dynam. Syst. (Rio de Janeiro, IMPA, Jan. 1992) (C. Camacho, ed.). Zbl0810.58036
  10. [E9] J. ECALLE, Alien calculus and its applications, three volumes in course of completion; scheduled to appear with Cambridge University Press. 
  11. [E10] J. ECALLE, Six lectures on transseries, analysable functions and the constructive proof of Dulac's conjecture, 75-184, in: Bifurcations and Periodic Orbits of Vector Fields (D. Schlomiuk, ed.), 1993, Kluwer Acad. Publ., NATO ASI Series, Series C, Vol. 408. Zbl0814.32008MR95d:34086
  12. [M] J. MARTINET, Normalisation des champs de vecteurs holomorphes, d'après A.D. Bryuno, Séminaire Bourbaki 1981-82, n° 582; Astérisque, 92-93 (1982), 59-73. 
  13. [S1] D. SCHLOMIUK, Algebraic particular integrals, integrability and the problem of the center, Trans. Amer. Math. Soc., 1993. Zbl0777.58028MR93j:34037
  14. [S2] D. SCHLOMIUK, Algebraic and geometric aspects of the theory of polynomial vector fields, 429-467, in: Bifurcations and Periodic Orbits of Vector Fields (D. Schlomiuk, ed.), 1993, Kluwer Acad. Publ., NATO ASI Series, Series C, Vol. 408. Zbl0790.34031MR95a:34042

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