Skip to main content

Travaux récents sur les points singuliers des équations différentielles linéaires

Part of the Lecture Notes in Mathematics book series (LNM,volume 770)

This is a preview of subscription content, access via your institution.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Bibliographie

  1. F. BALDASSARI-Differential modules and singular points of p-adic differential equations, (preprint).

    Google Scholar 

  2. W. BALSER, W. JURKAT, D. LUTZ-Birkhoff invariants and Stokes' Multipliers for meromorphic linear differential equations, (preprint).

    Google Scholar 

  3. G. BIRKHOFF-Singular points of ordinary differential equations, Trans. A.M.S., 10(1909), 436–470.

    CrossRef  MATH  MathSciNet  Google Scholar 

  4. G. BIRKHOFF-The generalized Riemann problem for linear differential equations, Proc. Am. Ac. A. Sc., 49(1913), 521–568.

    MATH  Google Scholar 

  5. D. CLARK-A note on the p-adic convergence of solutions of linear differential equations, Proc. A.M.S., 17(1966), 262–269.

    CrossRef  MATH  Google Scholar 

  6. E. CODDINGTON, N. LEVINSON-Theory of ordinary differential equations, Mc Graw Hill, 1955.

    Google Scholar 

  7. F. COPE-Formal solutions of irregular linear differential equations, II, Amer. J. Math., 58(1936), 130–140.

    CrossRef  MATH  MathSciNet  Google Scholar 

  8. P. DELIGNE-Equations différentielles à points singulaiers réguliers, Springer, Lecture Notes no 163, 1970.

    Google Scholar 

  9. P. DELIGNE-Lettres à Malgrange, (Août 1977 et Avril 1978).

    Google Scholar 

  10. B. DWORK, P. ROBBA-On ordinary linear p-adic differential equations, Trans. A.M.S., 231(1977), 1–46.

    CrossRef  MATH  MathSciNet  Google Scholar 

  11. A. ERDELYI-Asymptotic expansions, Dover, 1956.

    Google Scholar 

  12. A. GERARD, A. LEVELT-Invariants mesurant l'irrégularité en un point singulier des systèmes ..., Ann. Inst. Fourier, 23(1973), 157–195.

    MATH  MathSciNet  Google Scholar 

  13. B. HELFFER, Y. KANNAI-Determining factors and hypoellipticity ..., Astérisque, 2–3(1973), 197–216.

    MathSciNet  Google Scholar 

  14. M. HUKUHARA-Sur les points singuliers des équations différentielles linéaires, III, Mém. Fac. Sc. Kyusu Un., 2(1942), 125–137.

    MATH  MathSciNet  Google Scholar 

  15. E. INCE-Ordinary differential equations, Dover.

    Google Scholar 

  16. N. JACOBSON-Pseudo-linear transformations, Annals of Math., 38(1937), 484–507.

    CrossRef  MATH  Google Scholar 

  17. W. JURKAT, D. LUTZ-On the order of solutions of analytic linear differential equations, Proc. London M. S., 3(1971), 465–482.

    MathSciNet  Google Scholar 

  18. W. JURKAT-Meromorphe Differentialgleichungen, Springer Lecture Notes no 637, 1978.

    Google Scholar 

  19. N. KATZ-Nilpotent connections and the monodromy theorem ..., Publ. Math. IHES, no 39 (1970), 175–232.

    Google Scholar 

  20. N. KATZ-An overview of Deligne's work on Hilbert's 21rst problem, Proc. Symp. Pure Maths, 28(1976), 537–557.

    MATH  Google Scholar 

  21. H. KOMATSU-An introduction in the theory of hyperfunctions, in Proc. Conf. Katata, Springer Lecture Notes no 287 (1973), 3–40.

    Google Scholar 

  22. A. LEVELT-Jordan decomposition for a class of singular differential operators, Arkiv for Math., 13(1975), 1–27.

    CrossRef  MATH  MathSciNet  Google Scholar 

  23. K. MAHLER-Lectures on transcendental numbers, Springer Lecture Notes no 546, 1976.

    Google Scholar 

  24. B. MALGRANGE-Sur les points singuliers des équations différentielles linéaires, Enseign. math., 20(1970), 147–176.

    MathSciNet  Google Scholar 

  25. B. MALGRANGE-Remarques sur les équations différentielles à points singuliers irréguliers, Séminaire Goulaouic-Schwartz, 76–77, no 25.

    Google Scholar 

  26. B. MALGRANGE-Sur la réduction formelle des équations différentielles à singularités irrégulières, (preprint).

    Google Scholar 

  27. Yu. MANIN-Moduli fuchsiani, Ann. Sc. Norm. Pisa, III, 19(1965), 113–126.

    MATH  MathSciNet  Google Scholar 

  28. P.-D. MÉTHÉE-Systèmes différentiels du type de Fuchs en théorie des distributions, Comment. Math. Helv., 33(1959), 38–46.

    MATH  MathSciNet  Google Scholar 

  29. J. MOSER-The order of a singularity in Fuchs' theory, Math. Zeit., 72(1960), 379–398.

    CrossRef  MATH  Google Scholar 

  30. O. PERRON-Über lineare Differentialgleichungen mit rationalen Koeffizienten, Acta Math., 34(1911), 139–163.

    CrossRef  MATH  MathSciNet  Google Scholar 

  31. O. PERRON-Über Summengleichungen and Poincarésche Differenzengleichungen, Math. Ann., 84(1921), 1–15.

    CrossRef  MATH  MathSciNet  Google Scholar 

  32. J.-P. RAMIS-Dévissage Gevrey, Astérisque 59–60(1978), 173–204.

    MathSciNet  Google Scholar 

  33. J.-P. RAMIS-Sommation de séries divergentes, Séminaire Lelong-Skoda, 78–79.

    Google Scholar 

  34. P. ROBBA-Lemmes de Hensel pour les opérateurs différentiels, Séminaire Amice-Christol-Robba, 78–79.

    Google Scholar 

  35. Y. SIBUYA-Stokes phenomena, Bull. A.M.S., 83(1977), 1075–1077.

    CrossRef  MATH  MathSciNet  Google Scholar 

  36. Y. SIBUYA, S. SPERBER-Convergence of power series solutions of p-adic non-linear differential equations, (preprint).

    Google Scholar 

  37. H. TRJITZINSKY-Analytic theory of linear differential equations, Acta. Math., 62(1933), 167–226.

    CrossRef  MATH  MathSciNet  Google Scholar 

  38. H. TURRITIN-Convergent solutions of ordinary linear homogenous differential equations ..., Acta Math., 93(1955), 27–66.

    CrossRef  MathSciNet  Google Scholar 

  39. H. TURRITIN-Reduction of ordinary differential equations to the Birkhoff canonical form, Trans. A.M.S., 107(1963), 485–507.

    CrossRef  Google Scholar 

  40. W. WASOW-Asymptotic expansions for ordinary differential equations, Wiley, 1963.

    Google Scholar 

  41. G. WATSON-A theory of asymptotic series, Phil. Tr. R. Soc. A., 211(1912), 279–343.

    Google Scholar 

Download references

Authors

Rights and permissions

Reprints and Permissions

Copyright information

© 1980 N. Bourbaki

About this paper

Cite this paper

Bertrand, D. (1980). Travaux récents sur les points singuliers des équations différentielles linéaires. In: Séminaire Bourbaki vol. 1978/79 Exposés 525 – 542. Lecture Notes in Mathematics, vol 770. Springer, Berlin, Heidelberg . https://doi.org/10.1007/BFb0096245

Download citation

  • DOI: https://doi.org/10.1007/BFb0096245

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-09733-4

  • Online ISBN: 978-3-540-38547-9

  • eBook Packages: Springer Book Archive