The arborification-coarborification transform : analytic, combinatorial, and algebraic aspects
Annales de la Faculté des sciences de Toulouse : Mathématiques, Serie 6, Volume 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},
     mrnumber = {2116818},
     zbl = {1078.37016},
     language = {en},
     url = {http://www.numdam.org/item/AFST_2004_6_13_4_575_0/}
}
TY  - JOUR
AU  - Ecalle, Jean
AU  - Vallet, Bruno
TI  - The arborification-coarborification transform : analytic, combinatorial, and algebraic aspects
JO  - Annales de la Faculté des sciences de Toulouse : Mathématiques
PY  - 2004
SP  - 575
EP  - 657
VL  - 13
IS  - 4
PB  - Université Paul Sabatier, Institut de mathématiques
PP  - Toulouse
UR  - http://www.numdam.org/item/AFST_2004_6_13_4_575_0/
LA  - en
ID  - AFST_2004_6_13_4_575_0
ER  - 
%0 Journal Article
%A Ecalle, Jean
%A Vallet, Bruno
%T The arborification-coarborification transform : analytic, combinatorial, and algebraic aspects
%J Annales de la Faculté des sciences de Toulouse : Mathématiques
%D 2004
%P 575-657
%V 13
%N 4
%I Université Paul Sabatier, Institut de mathématiques
%C Toulouse
%U http://www.numdam.org/item/AFST_2004_6_13_4_575_0/
%G en
%F AFST_2004_6_13_4_575_0
Ecalle, Jean; Vallet, Bruno. The arborification-coarborification transform : analytic, combinatorial, and algebraic aspects. Annales de la Faculté des sciences de Toulouse : Mathématiques, Serie 6, Volume 13 (2004) no. 4, pp. 575-657. http://www.numdam.org/item/AFST_2004_6_13_4_575_0/

[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 | Zbl

[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

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

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

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

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

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

[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 | Zbl

[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 | Zbl

[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 | Zbl

[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

[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 | Zbl

[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 | Zbl

[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 | Zbl

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

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

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

[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 | Zbl

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

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