no. 5
The nilpotent part and distinguished form of resonant vector fields or diffeomorphisms
Annales de l'Institut Fourier, Volume 43 (1993) no. 5, pp. 1407-1483. 
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     title = {The nilpotent part and distinguished form of resonant vector fields or diffeomorphisms},
     journal = {Annales de l'Institut Fourier},
     pages = {1407--1483},
     publisher = {Institut Fourier},
     address = {Grenoble},
     volume = {43},
     number = {5},
     year = {1993},
     doi = {10.5802/aif.1379},
     zbl = {0816.30005},
     mrnumber = {95e:32046},
     language = {en},
     url = {https://aif.centre-mersenne.org/articles/10.5802/aif.1379/}
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Ecalle, J.; Schlomiuk, D. The nilpotent part and distinguished form of resonant vector fields or diffeomorphisms. Annales de l'Institut Fourier, Volume 43 (1993) no. 5, pp. 1407-1483. doi : 10.5802/aif.1379. https://aif.centre-mersenne.org/articles/10.5802/aif.1379/

[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). | Zbl

[E1] J. Ecalle, Les fonctions résurgentes, vol. 1, Algèbres de fonctions résurgentes, Publ. Math. Orsay, 1981. | Zbl

[E2] J. Ecalle, Les fonctions résurgentes, vol. 2, Les fonctions résurgentes appliquées à l'itération, Publ. Math. Orsay, 1981. | Zbl

[E3] J. Ecalle, Les fonctions résurgentes, vol. 3, L'équation du pont et la classification analytique des objets locaux, Publ. Math. Orsay, 1985. | Zbl

[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. | MR | Zbl

[E5] J. Ecalle, Introduction aux fonctions analysables et preuve constructive de la conjecture de Dulac, Actualités Math. Hermann, Paris, 1992.

[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.

[E7] J. Ecalle, Singularités non abordables par la géométrie, Ann. Inst. Fourier (Grenoble), 42 (1-2) (1992), 73-164. | Numdam | MR | Zbl

[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.). | Zbl

[E9] J. Ecalle, Alien calculus and its applications, three volumes in course of completion; scheduled to appear with Cambridge University Press.

[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. | MR | Zbl

[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. | Numdam

[S1] D. Schlomiuk, Algebraic particular integrals, integrability and the problem of the center, Trans. Amer. Math. Soc., 1993. | MR | Zbl

[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. | MR | Zbl

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