Local moduli for meromorphic differential equations

Babbitt, D. G. ; Varadarajan, V. S.

Astérisque, no. 169-170 (1989) , 221 p.

@book{AST_1989__169-170__1_0,
     author = {Babbitt, D. G. and Varadarajan, V. S.},
     title = {Local moduli for meromorphic differential equations},
     series = {Ast\'erisque},
     publisher = {Soci\'et\'e math\'ematique de France},
     number = {169-170},
     year = {1989},
     mrnumber = {1014083},
     zbl = {0683.34003},
     language = {en},
     url = {http://www.numdam.org/item/AST_1989__169-170__1_0/}
}

TY  - BOOK
AU  - Babbitt, D. G.
AU  - Varadarajan, V. S.
TI  - Local moduli for meromorphic differential equations
T3  - Astérisque
PY  - 1989
IS  - 169-170
PB  - Société mathématique de France
UR  - http://www.numdam.org/item/AST_1989__169-170__1_0/
LA  - en
ID  - AST_1989__169-170__1_0
ER  -

%0 Book
%A Babbitt, D. G.
%A Varadarajan, V. S.
%T Local moduli for meromorphic differential equations
%S Astérisque
%D 1989
%N 169-170
%I Société mathématique de France
%U http://www.numdam.org/item/AST_1989__169-170__1_0/
%G en
%F AST_1989__169-170__1_0

Babbitt, D. G.; Varadarajan, V. S. Local moduli for meromorphic differential equations. Astérisque, no. 169-170 (1989), 221 p. http://numdam.org/item/AST_1989__169-170__1_0/

Bibliographie
Cité par

[A] E. Artin, Algebraic Numbers and Algebraic Numbers, Gordon and Breach, New York 1957. | MR

[Bal] W. Balser, Zum Einzigkeitssatz in der Invariantentheorie meromorpher Differentialgleichungen, Journal für die reine und angewandte Mathematik, 318 (1980), 51-82. | MR | Zbl | EuDML

[Be] D. Bertrand, Travaux récents sur les points singuliers des équations différentielles linéaires, Sém. Bourbaki 1978/79, Exp. 525-542, Lecture Notes in Mathematics, No. 770, Springer-Verlag, 1980. | DOI | MR | Zbl | EuDML | Numdam

[BJL] W. Balser, W. Jurkat, and D. A. Lutz, A general theory of invariants for meromorphic differential equations ; Part II, Proper invariants, Funkcialaj Ekvacioj 22 (1979), 257-283. | MR | Zbl

[BM] S. Bochner and W. T. Martin, Several Complex Variables, Princeton University Press, Princeton, N. J. 1948. | MR | Zbl

[Bo] A. Borel, Linear Algebraic Groups, W. A. Benjamin, New York 1969. | MR | Zbl

[BV 1] D. G. Babbitt and V. S. Varadarajan, Formal reduction of meromorphic differential equations : a group theoretic view, Pacific J. Math., 108 (1983), 1-80. | MR | Zbl | DOI

[BV 2] D. G. Babbitt and V. S. Varadarajan, Deformations of nilpotent matrices over rings and reduction of analytic families of meromorphic differential equations, Mem. Amer. Math. Soc., Vol. 55, No. 325, 1985. | MR | Zbl

[BV 3] D. G. Babbitt and V. S. Varadarajan, Local moduli for meromorphic differential equations, Bull. Amer. Math. Soc., 12 (New Series) (1985), 95-98. | MR | Zbl | DOI

[BV 4] D. G. Babbitt and V. S. Varadarajan, Local moduli for meromorphic differential equations. I. The Stokes sheaf and its cohomology, UCLA Preprint, 1985. | Zbl | MR

[BV 5] D. G. Babbitt and V. S. Varadarajan, Local isoformal deformation theory for meromorphic differential equations near an irregular singularity. Deformation theory of algebras and structures and applications, 583-700. NATO ASI Series, Series C. Mathematical and Physical Sciences - Vol. 247. (ed) Michiel Hazewinkel and Murray Gerstenhaber. Kluver Academic Publishers, 1988. | MR | Zbl | DOI

[BV 6] D. G. Babbitt and V. S. Varadarajan, Some remarks on the asymptotic existence theorem for meromorphic differential equations, Submitted to the Journal of the Faculty of Science, University of Tokyo, Sect. I A. | MR | Zbl

[Co 1] F. T. Cope, Formal solutions of irregular linear differential equations I, Amer. J. Math., 56 (1934), 411-437. | MR | JFM | DOI

[Co 2] F. T. Cope, Formal solutions of irregular Inear differential equations, II, Amer. J. Math., 58 (1936), 130-140. | MR | JFM | DOI

[De 1] P. Deligne, Equations Différentielles à points singuliers Réguliers, Lecture Notes in Mathematics, No. 163, Springer-Verlag, 1970. | Zbl | MR

[De 2] P. Deligne, Letters to Malgrange, 1977-1978.

[De 3] P. Deligne, Letter to Varadarajan, 1986.

[Di] J. Dieudonné, Cours de Géométrie Algébrique, Presses Universitaires de France, Paris 1974. | Zbl

[DM] A. Duval and C. Mitschi, Matrices de Stokes et groupe de Galois des équations hypergéometriques confluents generalisées, to appear in the Pacific Journal of Mathematics. | MR | Zbl

[Fa] E. Fabry, Sur les intégrales des équations différentielles linéaires à coefficients rationnels, Thèse, Paris, 1885.

[G] R. Godement, Topologie Algébrique et Théorie des Faisceaux, Hermann, Paris 1958. | MR | Zbl

[Hu 1] M. Hukuhara, Sur les points singuliers des équations différentielles linéaires, II, Jour, Fac. Sci. Hokkaido Univ, 5 (1937), 123-166. | JFM | DOI

[Hu 2] M. Hukuhara, Sur les points singuliers des équations différentielles linéaires, III, Mem. Fac. Sci. Kyushu Univ., 2 (1942), 125-137. | MR | Zbl

[J] W. Jurkat, Meromorphe Differentialgleichungen, Lecture Notes in Mathematics, No. 637, Springer-Verlag, 1978. | MR | Zbl

[Ka] N. Katz, Nilpotent connections and the monodromy theorem : application of a result of Turrittin, Pub. Math. I.H.E.S., 39 (1970), 207-238. | MR | Zbl | EuDML | Numdam

[Le] A. H. M. Levelt, Jordan decomposition for a class of singular differential operators, Ark. Math., 13 (1975), 1-27. | MR | Zbl | DOI

[Ma] Yu. Manin, Moduli fuchsiani, Ann. Sc. Norm. Sup. Pisa, 19 (1965), 113-126. | MR | Zbl | EuDML | Numdam

[Maj] H. Majima, Asymptotic Analysis for Integrable Connections with Irregular Singular Points, Lecture Notes in Mathematics, No. 1075, Springer-Verlag, 1984. | MR | Zbl

[Mal 1] B. Malgrange, Sur les points singuliers des équations différentielles, L'Enseignment Math., 20, (1974), 147-176. | MR | Zbl

[Mal 2] B. Malgrange, Sur le réduction formelle des équations à singularités irrégulières, Grenoble preprint, 1979.

[Mal 3] B. Malgrange, Remarques sur les équations différentielles à points singulier irréguliers, in Equations Différentielles et Systèmes de Pfaff dans le champ complexe, R. Gérard et J.-P. Ramis, Eds., Lecture Notes in Mathematics No. 712, Springer-Verlag, 1979. | DOI | MR | Zbl | Numdam

[Mal 4] B. Malgrange, La classification des connexions irréguliers à une variable, in Mathématique et Physique : Sém. Ecole Norm. Sup. 1979-82, Birkhäuser, 1983. | MR | Zbl

[Malm] J. Malmquist, Sur l'étude analytique des solutions d'un système des équations différentielles dans le voisinage d'un point singulier d'indétermination, I, Acta Math., 73 (1940), 8-129. | MR | Zbl | JFM

J. Malmquist, Sur l'étude analytique des solutions d'un système des équations différentielles dans le voisinage d'un point singulier d'indétermination, II, Acta Math., 74 (1941), 1-64. | MR | Zbl | JFM | DOI

J. Malmquist, Sur l'étude analytique des solutions d'un système des équations différentielles dans le voisinage d'un point singulier d'indétermination, III, Acta Math., 74 (1941), 109-128. | MR | Zbl | JFM | DOI

[MF] D. Mumford and J. Fogarty, Geometric Invariant Theory, 2nd Enl. Ed., Springer-Verlag, 1982. | MR | Zbl

[Mi] B. Mitchell, Theory of Categories, Academic Press, New York and London 1965. | MR | Zbl

[MK] J. Morrow and K. Kodaira, Complex Manifolds, Holt, Rinehart and Winston, New York 1971. | MR | Zbl

[MR] J. Martinet and J-P. Ramis, Problèmes de modules pour des équations différentielles non-linéaires du premier ordre, Publ. Math. I.H.E.S. 55 (1982), 63-164. | DOI | MR | Zbl | EuDML | Numdam

[Po] H. Poincaré, Sur les intégrales des équations linéaires, Acta Math., 8 (1886), 295-344. | MR | JFM | DOI

[Ra 1] J-P. Ramis, Les series $k$ -sommables et leurs applications, in Complex Analysis, Microlocal Calculus and Relativistic Quantum Theory. Proceedings 1979, Ed. by D. Iagolnitzer, Lecture Notes in Physics, No. 126, Springer-Verlag, 1980. | MR | Zbl | DOI

[Ra 2] J-P. Ramis, Théorèmes d'indices Gevrey pour les équations différentielles ordinaires, Mem. Amer. Math Soc., Vol. 48, No. 296, 1984. | MR | Zbl

[Ra 3] J-P. Ramis, Phénomène de Stokes et resommation, C. R. Acad. Sci. Paris, t. 301, Sér.I. n° 4 (1985), 99-102. | MR | Zbl

[Ra 4] J-P. Ramis, Phénomène de Stokes et filtration Gevrey sur le groupe de Picard-Vessiot, C. R. Acad. Sci, Paris, t. 301, Sér. I, n° 5 (1985), 165-167. | MR | Zbl

[Ra-Si] J-P. Ramis and Y. Sibuya, Hukuhara's domains and fundamental existence and uniqueness theorems for asymptotic solutions of Gevrey type, To appear in Asymptotic Analysis, 2 (1), 1989. | MR | Zbl

[Ro] P. Robba, Lemmes de Hensel pour les opérateurs différentials. Application à la réduction formelle des équations différentielles, L'Enseignement, 26 (1980), 279-311. | MR | Zbl

[Se] J. P. Serre, Corps Locaux, Actualités sci. ind, 1296, Hermann, Paris 1968. | MR

[Ses] C. S. Seshadri, Theory of moduli, in Proceedings of Symposia in Pure Mathematics, Vol XXIX, Amer. Math. Soc. 1975, pp. 263-304. | MR | Zbl | DOI

[Si 1] Y. Sibuya, Simplification of a System of linear ordinary differential equations about a singular point, Funkcialaj Ekvacioj, 4 (1962), 29-56. | MR | Zbl

[Si 2] Y. Sibuya, Stokes phenomena, Bull. Amer. Math. Soc, 83 (1977), 1075-1077. | MR | Zbl | DOI

[Tri] W. J. Trijitzinsky, Analytic theory of linear differential equations, Acta Math., 62 (1934), 167-226. | MR | JFM | DOI

[Tu] H. Turrittin, Convergent solutions of ordinary differential equations in the neighborhood of an irregular singular point, Acta Math., 93 (1955), 27-66. | MR | Zbl | DOI

[V] V. S. Varadarajan, Lie Groups, Lie Algebras, and Their Representations, Graduate Texts in Mathematics No. 102, Springer-Verlag, 1984. | MR | Zbl

[W] W. Wasow, Asymptotic Expansions for Ordinary Differential Equations, Interscience, New York, 1965. | MR | Zbl

[Wa] W. C. Waterhouse, Introduction to Affine Group Schemes, Graduate Texts in Mathematics, No. 66, Springer-Verlag, 1979. | MR | Zbl

[WW] E. T. Whittaker and G. N. Watson, A Course in Modern Analysis. 4th Edition, Cambridge University Press, London 1963. | MR | Zbl

[ZS] O. Zariski and P. Samuel, Commutative Algebra, Vol. 1, Van Nostrand, Princeton, N.J. 1958. | MR