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The arborification-coarborification transform : analytic, combinatorial, and algebraic aspects
Annales de la Faculté des sciences de Toulouse : Mathématiques, Série 6, Tome 13 (2004) no. 4, pp. 575-657.
@article{AFST_2004_6_13_4_575_0,
     author = {\'Ecalle, Jean and Vallet, Bruno},
     title = {The arborification-coarborification transform : analytic, combinatorial, and algebraic aspects},
     journal = {Annales de la Facult\'e des sciences de Toulouse : Math\'ematiques},
     pages = {575--657},
     publisher = {Universit\'e Paul Sabatier, Institut de Math\'ematiques},
     address = {Toulouse},
     volume = {Ser. 6, 13},
     number = {4},
     year = {2004},
     doi = {10.5802/afst.1083},
     zbl = {1078.37016},
     mrnumber = {2116818},
     language = {en},
     url = {https://afst.centre-mersenne.org/articles/10.5802/afst.1083/}
}
Jean Ecalle; Bruno Vallet. The arborification-coarborification transform : analytic, combinatorial, and algebraic aspects. Annales de la Faculté des sciences de Toulouse : Mathématiques, Série 6, Tome 13 (2004) no. 4, pp. 575-657. doi : 10.5802/afst.1083. https://afst.centre-mersenne.org/articles/10.5802/afst.1083/

[Braa] Braaksma ( S.). - Multisummability of formal power series solutions of non-linear meromorphic differential equations, Ann. Inst. Fourier, Grenoble, 42, p. 517-540 (1992). | Numdam | MR 1182640 | Zbl 0759.34003

[Br] Bryuno (A.D. ) (often transliterated as Bruno or Brjuno). - Analytical forms of differential equations, I,II, Trudy Mosk. Mat. Ob. 25 (1971), 119-262, 26 (1972), p. 199-239; English translation in Trans. Mosc. Soc. 25 ; 26 (1971 ; 1972)

[E1] Ecalle (J. ). - Les fonctions résurgentes, Vol.1, Algèbres de fonctions résurgentes, Publ. Math. Orsay ( 1981). | Zbl 0499.30034

[E2] Ecalle (J. ). - Les fonctions résurgentes, Vol.2, Les fonctions résurgentes appliquées à l'itération, Publ. Math. Orsay (1981). | Zbl 0499.30035

[E3] Ecalle (J. ). - Les fonctions résurgentes, Vol.3, L'équation du pont et la classification analytique des objets locaux, Publ. Math. Orsay (1985). | MR 852210 | Zbl 0602.30029

[E4] Ecalle (J. ). - The acceleration operators and their applications , Proc. Internat. Cong. Math., Kyoto (1990), vol.2, Springer , Tokyo, p. 1249-1258 (1991 ). | MR 1159310 | Zbl 0741.30030

[E5] Ecalle (J. ). - Singularités non abordables par la géometrie , Ann. Inst. Fourier, Grenoble, 42, p. 73-164 (1992). | Numdam | MR 1162558 | Zbl 0940.32013

[E6] Ecalle (J. ). - Introduction aux fonctions analysables et preuve constructive de la conjecture de Dulac, Actual. Math., Hermann, Paris (1992). | MR 1399559

[E7] Ecalle (J. ). - Weighted products and parametric resurgence , in: Méthodes résurgentes, Travaux en Cours, 47, p. 7-49, Ed. L. Boutet de Monvel (1994). | MR 1296470 | Zbl 0834.34067

[E8] Ecalle (J. ). - Compensation of small denominators and ramified linearisation of local objects, in : Complex Analytic Methods in Dynamical Systems, IMPA, Jan 1994, Aster., p. 135-199 (1994). | MR 1285388 | Zbl 0810.58036

[E9] Ecalle (J. ). - Six Lectures on Transseries, Analysable Functions and the Constructive Proof of Dulac's Conjecture, Bifurcations and Periodic Orbits of Vector Fields, D. Schlomiuk ed., p. 75-184, Kluwer (1993). | MR 1258519 | Zbl 0814.32008

[E10] Ecalle (J. ). - Recent Advances in the Analysis of Divergence and Singularities, Normal Forms, Bifurcations and Finiteness Problems in Differential Equations , Yu. Ilyashenko and C. Rousseau ed., p. 87-186, Kluwer (2003). | MR 2083246

[E11] Ecalle (J. ). - Twisted Resurgence Monomials and canonical synthesis of Local Objects, to appear in the Proc. of the June 2002 Edinburgh conference on Analysable Functions, World Scientific , O. Costin Ed.

[EM] Ecalle (J. ) , Menous ( F.) . - Well-behaved convolution averages, in: The Stokes Phenomenon and Hilbert's 16th Problem , eds B.L.J. Braaksma, G.K. Immink , M. van der Put, p. 71-101, World Scient. Publ. | MR 1443689 | Zbl 0857.34009

[EV1] Ecalle (J. ) , Vallet ( B.) . - Prenormalisazation, correction, and linearization of resonant vector fields or diffeomorphisms , Prepubl. Orsay (1995).

[EV2] Ecalle ( J.), Vallet (B.). - Correction, and linearization of resonant vector fields or diffeomorphisms, Math. Z. 229, p. 249-318 (1998). | MR 1652158 | Zbl 0921.32014

[EV3] Ecalle (J. ) , Vallet ( B.J.). - Intertwined Mappings, Also in these same Luminy-2003 Proceedings, Vol. 1. | Numdam

[El1] Eliasson ( L.H. ). - Generalization of an estimate of small divisors by Siegel, in Rabinowitz, Zehnder (eds.), Analysis et cetera (sic, Academic Press (1990). | MR 1039350 | Zbl 0703.34010

[EL2] Eliasson ( L.H. ). - Hamiltonian systems with linear form near an invariant torus,Turchetti Ed., Non-linear Dynamics, World Scientific, Singapore (1989). | MR 1115677 | Zbl 0744.58019

[E13] Eliasson ( L.H.). - Floquet solutions for the one-dimensional quasiperiodic Schrödinger equation, Comm. Math. Phys. 146, p. 447-482 (1992). | Zbl 0753.34055

[Kri] Krikorian ( R.). - Réductibilité des systèmes produits-croisés à valeurs dans des groupes compacts, Soc. Math. France , Astérisque, 0259 (1999). | Zbl 0957.37016

[Mel] Menous (F. ) . - Les bonnes moyennes uniformisantes et leurs applications à la resommation réelle, PhD Thesis , Orsay (1996).

[Me2] Menous (F. ) . - An example of local analytic q-difference equation : Analytic classification, Prepub. Orsay, ( 2003-81).

[Sie1] Siegel ( C.L.). - Iteration of analytic functions, Ann. Math. 43, p. 607-612 (1942). | MR 7044 | Zbl 0061.14904

[Sie2] Siegel ( C.L.). - Über die Normalform analytischer Differentialgleichungen in der Nähe einer Gleichgewichtslösung, Nachr. Akad. Wiss. Göttingen Math.Phys. Abt. (1952). | Zbl 0047.32901

[Ru] Rüssmann. - Über die Iteration analytischer Funktionen, J. Math. Mech. 17, p. 523-532 (1967). | Zbl 0186.47704