Main publications :


  1. Théorie des invariants holomorphes.
    Thèse d'Etat, Orsay, March 1974.

  2. Théorie iterative: introduction à la théorie des invariants holomorphes.
    J. Math. pures et appl., 54, 1975, p. 183-258.

  3. The main results about holomorphic invariants were announced in:
    C.R.A.S., t. 272, A 1971, p 225-228
    C.R.A.S., t. 272, A 1971, p 308-311
    C.R.A.S., t. 272, A 1971, p 372-375
    C.R.A.S., t. 276, A 1973, p 179-182
    C.R.A.S., t. 276, A 1973, p 261-264
    C.R.A.S., t. 276, A 1973, p 375-378
    C.R.A.S., t. 276, A 1973, p 471-474
    Vestnik L.G.U., 7 1973, p 69-71
    Vestnik L.G.U., 13 1973, p 166-169

  4. Some new criteria for the Riemann hypothesis:
    C.R.A.S., t. 277, A 1973, p 23-25

  5. The seminal ideas behind resurgence theory were set forth in:
    C.R.A.S., t. 282, A 1976, p 203-206
    C.R.A.S., t. 282, A 1976, p 861-864
    C.R.A.S., t. 282, A 1976, p976-982
    Un analogue distant des fonctions automorphes: les fonctions résurgentes,
    Séminaire Choquet,1977-78.

  6. Les fonctions résurgentes, Vol. 1:
    Algèbres de fonctions résurgentes.

    Publ. Math. Orsay 81.05 (1981), # 248 pp.

  7. Les fonctions résurgentes, Vol. 2:
    Les fonctions résurgentes appliquées à l'itération.

    Publ. Math. Orsay 81.06 (1981), # 283 pp.

  8. Les fonctions résurgentes, Vol. 3:
    L'équation du pont et la classification analytique des objets locaux.

    Publ. Math. Orsay 85.05 (1985), # 585 pp.

  9. Iteration and analytic classification of local diffeomorphisms of C^n.
    in Iteration theory and its functional equations. Lecture Notes 1163, Springer, 1985, p 41-48.

  10. Cinq applications des fonctions résurgentes.
    Prepub. Math. d'Orsay, 1984, 84T62, # 110 pp.
    One of these five articles is available here: Singularités irrégulieres et résurgence multiple.

  11. Classification analytique des champs hamiltoniens. Potentiels de résurgence et hamiltoniens étrangers.
    Proc. of the Dijon 1985 Conference on Differential Equations in the Complex Field, Asterisque.

  12. L'accélération des fonctions résurgentes,
    Unpublished typescript, Orsay 1985, # 54 pp.
    A scan of the original typescript (-unpublished because unsubmitted, and unsubmitted
    because widely circulated and then half-forgotten-) can be accessed here.
    We didn't attempt to bring the text in line with our later notations and nomenclature on accelaration theory.

  13. (with J. Martinet, R. Moussu, J.-P. Ramis)
    Non-accumulation des cycles-limites.
    C.R.A.S., t. 304, série I,no 14, 1987, p 375-378
    C.R.A.S., t. 304, série I,no 14, 1987, p 431-434

  14. Finitude des cycles limite et accéléro-sommation de l'application de retour.
    Bifurcations of Planar Vector Fields, Proceedings, Luminy 1989, Lecture Notes 1455, Springer, p 74-159.

  15. The acceleration operators and their applications. Proc. Internat. Cong. Math., Kyoto, 1990, vol.2, Springer, Tokyo, 1991, p1249-1258.

  16. The Bridge Equation and its Applications to Local Geometry.
    in Proc. of the Intern. Confer. on Dynamical Systems and Related Topics, K. Shiraiwa ed.,
    Advanced Series in Dynamical Systems, Vol.9, 1991, p 100-122.

  17. Singularités non abordables par la géométrie.
    Ann. Inst. Fourier,Grenoble, 42, 1992, p 73-164.

  18. Introduction aux fonctions analysables et preuve constructive de la conjecture de Dulac.
    (book), Actual. Math., Hermann, Paris, 1992, # 337 pp.
    The contents of the book, along with an update, are described in Dulac: constructive proof .
    The book itself can be downloaded from this portal .

  19. 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, 1993, Kluwer

  20. Discretised Resurgence.
    Annexe C, p 161-218,
    Included in F. Menous' PhD Thesis:
    Les bonnes moyennes uniformisantes et leurs applications à la resommation réelle
    PhD Thesis, 26.5.1999, Laboratoir Emile Picard, Université P. Sabatier, Toulouse, France.

  21. Cohesive functions and weak accelerations.
    Journal d'Analyse Mathématique, Vol. 60 (1993), p 71-97.

  22. (with D. Schlomiuk)
    The nilpotent part and distinguished form of resonant vector fields or diffeomorphisms.
    Annales de Institut Fourier, 1993, p 1407-1483.

  23. Weighted products and parametric resurgence
    in Méthodes résurgentes, Travaux en Cours, 47, L. Boutet de Monvel ed., 1994, p 7-49.

  24. Compensation of small denominators and ramified linearisation of local objects.
    in Complex Analytic Methods in Dynamical Systems, IMPA, Asterisque, 1994, p 135-199.

  25. (with F. Menous)
    Well-behaved convolution averages and the non-accumulation theorem for limit-cycles.
    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.

  26. (with B. Vallet)
    Passive/active resonance. Non-linear resurgence and isoresurgent deformations.
    in: The Stokes Phenomenon and Hilbert's 16th Problem, eds B.L.J. Braaksma, G.K. Immink, M. van der Put, p ...-..., World Scient. Publ.

  27. Prenormalisazation, correction, and linearization of resonant vector fields or diffeomorphisms.
    Prepub. Orsay 95-32 (1995), # 90 pp.

  28. (with B. Vallet)
    Correction, and linearization of resonant vector fields or diffeomorphisms.
    Math. Zeitschrift 229, p 249-318 (1998)

  29. A Tale of Three Structures: the Arithmetics of Multizetas, the Analysis of Singularities, the Lie Algebra ARI.
    Diff. Eq. and the Stokes Phenomenon, BLJ Braaksma, GK Immink, M van der Put, J Top Eds 2002, World Scient. Publ.,p 89-146.

  30. Recent Advances in the Analysis of Divergence and Singularities.
    Proceedings of the July 2002 Montreal Seminar on Bifurcations, Normal forms and Finiteness Problems in Differential Equations,
    C. Rousseau,Yu. Ilyashenko Publ., 2004 Kluwer Acad. Publ., p 87-187

  31. ARI/GARI. la dimorphie et l'arithmétique des multizetas: un premier bilan.
    Journal de Théorie des Nombres de Bordeaux, 15 (2003), p 411-478.

  32. Twisted Resurgence Monomials and canonical-spherical synthesis of Local Objects.
    Proc. of the June 2002 Edinburgh conference on Asymptotics and Analysable Functions, O. Costin ed, World Scient. Publ., # 105 pp

  33. (with B. Vallet)
    Intertwined mappings.
    prepub. Orsay 2003-73, # 92 pp.
    Ann. Fac. Sc. Toulouse,  Tome XIII, no 3 (2004),  p. 291-376.

  34. (with B. Vallet)
    The arborification-coarborification transform: analytic, combinatorial. and algebraic aspects
    prepub. Orsay 2004-30, # 80 pp
    Ann. Fac. Sc. Toulouse, Ser.6, 13, no 4 (2004), p. 575-657.

  35. Multizetas, perinomal numbers, arithmetical dimorphy, and ARI/GARI.
    prepub. Orsay 2004-37, # 26 pp (a survey)
    Ann. Fac. Sc. Toulouse, Tome XIII, no. 4 (2004), p. 683-708.

  36. (with Sh. Sharma)
    Power series with sum-product Taylor coefficients and their resurgence algebra.
    prepub. Orsay 2010-04, # 146 pp
    Ann.Scuo.Norm.Pisa , 2011, Vol.1, Asymptotics in Dynamics, Geometry and PDEs; Generalized Borel Summation; ed. O.Costin, F.Fauvet, F.Menous, D.Sauzin.

  37. The flexion structure and dimorphy: flexion units, singulators, generators, and the enumeration of multizeta irreducibles.
    prepub. Orsay 2010-05, # 163 pp.
    Ann.Scuo.Norm.Pisa , 2011, Vol.2, Asymptotics in Dynamics, Geometry and PDEs; Generalized Borel Summation; ed. O.Costin, F.Fauvet, F.Menous, D.Sauzin.
    An enlarged version, March 2011, # 185 pp, can be found here and the penultimate galley proof is here.

  38. (X. Buff, J. Ecalle, A. Epstein)
    Limits of Degenerate Parabolic Quadratic Rational Maps.
    Final version 2012-08, # 46 pp
    To appear in Geometric and Functional Analysis.

  39. (with O. Bouillot)
    Invariants of identity-tangent diffeomorphisms: explicit formulae and effective computation.
    Orsay 2012-07, # 42 pp

  40. Eupolars and their bialternality grid.  Appeared in A.M.V., 2015.
    A preliminary version (# 85 pp) was posted in February 2014 and slightly expanded in March 2014.
    The complete version (# 114 pp) was posted in April 2014.
    Numerous illustrative Tables can be accessed here or here.

  41. Singulators vs Bisingulators. (# 21 pp, 7 June 2014)
    This is a preview of the last chapter of a forthcoming monograph:
    Finitary Flexion Algebras. (to be posted in July 2014)

  42. Singularly Perturbed Systems, Coequational Resurgence, and Flexion Operations. (# 21 pp, 7 June 2014)
    This is a preview of the first part of a larger monograph:
    The Three Bridge Equations (forthcoming).

  43. Singular ODEs and Resurgence. (June 2015)
    (in Russian)

  44. The Natural Growth Scale. (January 2016,145 pp)
    Updated in March 2018.

  45. Combinatorial tidbits from resurgence theory and mould calculus. (June 2016, 36 pp)
    Based on a series of talks delivered at a meeting of combinatoricists.
    1. From moulds to bimoulds, and back.
    2. Mould extensions of classical functions.
    3. Natural projectors.
    4. Minimal convolution domains.
    5. Iso-differential operators and their natural basis.

  46. Invariants of identity-tangent diffeomorphisms expanded as series of multitangents and multizetas. (November 2016, 120 pp)

  47. Taming the coloured multizetas. (forthcoming).
  48. Here are the slides of a talk given on 27/06/2017 at CIRM (Marseilles-Luminy).
    The comments on the black-numbered, star-marked slides were added after the event.
    A full exposition can be found in the chapters 1 and 4 of this long paper.

  49. The scrambling operators applied to multizeta algebra and singular perturbation analysis. (October 2018, 156 pp).
    The scrambling operators applied to multizeta algebra and singular perturbation analysis. (expanded version, March 2019, 203 pp).
    (i) Gives a synopsis of the three scrambling operators (scram, viscram, discram) and applies them:
    (ii) to the theory of singular pertubations, to derive the Second and Third Bridge Equations in the most general situation,
    (iii) to multizeta algebra, to show (among other results) how the complete set of coloured multizetas can be recovered from any of three small subsets of boundary data (known as "satellites").
    For a survey of the chapters on bicoloured multizetas (ch.3-4 of the 2018 version; ch. 5-7 of the 2019 version), see these slides .
    For a survey of the chapters on singular perturbations (ch. 2 of the 2018 version; ch. 3-4 of the 2019 version) see these slides .
    A compact exposition of the question is also available in sections 2-8 of here , while sections 9-11 contain new material.

  50. Resurgent analysis of singularly perturbed systems: exit Stokes, enter Tes. (25 pp).
    To appear in the Proceedings of the Nov. 2018 Moscow Conference in Memory of Prof. B. Yu. Sternin.
    For the related slides, go there .

  51. Coequational resurgence's three surprises: tessellation, isography, autarchy. (25 pp).
    To appear. Much of the material is already covered in the preceding two publications, but this one shall present numerous examples and complements. Pending the full text, here are the slides of a related talk (IHES, June 2019):
    Resurgence's two main types and their signature complications: tessellation, isography, autarchy. .






    FORTHCOMING



    A --- Book series on resummation theory and the underlying structures.

  52. Vol 0. Resummation calculus. (Compact Survey of Vol. 1-5.)

  53. Vol 1. Mould calculus.

  54. Vol 2. Resurgent functions and alien derivations. Main applications.

  55. Vol 3. Acceleration theory and its main applications.

  56. Vol 4. Monotonous Analysis. Transseries and analysable functions. Accelero-synthesis and decelero-analysis.

  57. Vol 5. Applications to Local Objects. The Bridge Equation.





  58. B --- Book series on numerical dimorphy, multizeta arithmetic, ARI-GARI and the flexion structure.

  59. Vol 0. The Flexion Structure and Dimorphy. (Compact Survey of Vol. 1-4.)

  60. Vol 1. ARI/GARI and the flexion structure.

  61. Vol 2. ARI/GARI and its special bimoulds.

  62. Vol 3. Explicit-canonical decomposition of multizetas into irreducibles.

  63. Vol 4. Perinomal numbers and multizeta irreducibles.





Related publications by others :