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Pacific Journal of Mathematics

Formal reduction theory of meromorphic differential equations: a group theoretic view.

Donald G. Babbitt and V. S. Varadarajan

Source: Pacific J. Math. Volume 109, Number 1 (1983), 1-80.

Primary Subjects: 34A20
Secondary Subjects: 12H05, 14D05, 14D25

Full-text: Open access

Links and Identifiers

Permanent link to this document: http://projecteuclid.org/euclid.pjm/1102720203
Zentralblatt MATH identifier: 0533.34010
Mathematical Reviews number (MathSciNet): MR716289

References

[1] D. Bertrand, Traaux recents sur les points singuliers des equations differentielles lineaires, Sem. Bourbaki, 1978/79, Exposes 525-542, Lecture Notes in Mathematics No. 770, Berlin, Heidelberg,1980.
Mathematical Reviews (MathSciNet): MR82a:34007
Zentralblatt MATH: 0445.12012
[2] G. D. Birkhoff, Equivalent singular points of ordinary linear differential equations, Math. Ann., 74 (1913), 134-139, Collected Mathematical Papers, Vol. 1, pp. 252-257, Dover Publications, New York, 1968.
Zentralblatt MATH: 44.0373.01
[3] A. Borel, Linear Algebraic Groups, W. A. Benjamin, New York, 1969.
Mathematical Reviews (MathSciNet): MR40:4273
[4] N. Bourbaki, Elements des Mathematiques, Livre II, Algebra Ch. 6-7 (2nd Ed.), Hermann, Paris.
Zentralblatt MATH: 0181.29201
[5] E. Coddington, and N. Levinson, Theory of Ordinary Differential Equations, McGraw- Hill, New York, 1955.
Mathematical Reviews (MathSciNet): MR16:1022b
[6] F. Cope, Formal solutions of irregular linear differential equations, Amer. J. Math., 58 (1936), 130-140.
Zentralblatt MATH: 59.0447.12
[7] P. Deligne, Equations Differentielles a Points Singuliers Reguliers, Lecture Notes in Mathematics, No. 163, Springer-Verlag, Berlin, Heidelberg,1970.
Mathematical Reviews (MathSciNet): MR54:5232
Zentralblatt MATH: 0244.14004
[8] F. R. Gantmacher, Theory of Matrices, Vol. I, Chelsea,New York, 1959.
Mathematical Reviews (MathSciNet): MR99f:15001
[9] F. R. Gantmacher, Theory of Matrices, Vol. II, Chelsea,New York, 1959-60.
Mathematical Reviews (MathSciNet): MR99f:15001
[10] Harish-Chandra, Invariant distributions on Lie algebras, Amer. J. Math., 86 (1964), 271-309.
Mathematical Reviews (MathSciNet): MR28:5144
Zentralblatt MATH: 0131.33302
[11] W. Jurkat, Meromorphe Differentialgleichungen, Lecture Notes in Mathematics, No. 637, Springer-Verlag,Berlin, Heidelberg,1978.
Mathematical Reviews (MathSciNet): MR82a:34004
Zentralblatt MATH: 0408.34004
[12] W. Jurkat, and D. Lutz, On the order of solutions of analytic linear differential equations, Proc. London Math. Soc, 3 (1971),465-482.
Mathematical Reviews (MathSciNet): MR44:4269
Zentralblatt MATH: 0246.34009
[13] N. M. Katz, Nilpotent connections and the monodromy theorem: Applications of a result of Turrittin, Publ. Math. IHES, No. 39 (1970), 175-232.
Mathematical Reviews (MathSciNet): MR45:271
Zentralblatt MATH: 0221.14007
[14] B. Kostant, The principal three-dimensional subgroup and the Betti numbers of a complex simple Lie group, Amer. J. Math., 81 (1959),973-1032.
Mathematical Reviews (MathSciNet): MR22:5693
Zentralblatt MATH: 0099.25603
[15] B. Kostant, Lie group representations on polynomial rings, Amer. J. Math., 85 (1963), 327-404.
Mathematical Reviews (MathSciNet): MR28:1252
Zentralblatt MATH: 0248.20056
[16] A. Levelt,Jordan decomposition for a class of singular differential operators, Arkiv for Math., 13(1975), 1-27.
Mathematical Reviews (MathSciNet): MR58:17962
Zentralblatt MATH: 0305.34008
[17] D. Lutz, Asymptotic behavior of solutions of linear systems of ordinary differential equations near an irregular singular point, Amer. J. Math., 91 (1969),95-105.
Mathematical Reviews (MathSciNet): MR39:3076
Zentralblatt MATH: 0183.35905
[18] Yu Manin, Moduli fuchsiani, Ann. Sc. Norm. Pisa, III,19 (1965), 113-126.
Mathematical Reviews (MathSciNet): MR31:4815
Zentralblatt MATH: 0166.04301
[19] J. Moser, The order of a singularity in Fuchs' theory, Math. Z., 72 (1960), 379-398.
Mathematical Reviews (MathSciNet): MR22:8155
Zentralblatt MATH: 0117.04902
[20] H. Poincare, Sur les integrals irregulieres des equations lineaires, Acta Math., 8 (1886), 295-344, Oeuvres de Henri Poincare, Tome 1, pp. 290-332, Gauthier-Villars, Paris, 1928.
Zentralblatt MATH: JFM 18.0273.02
[21] L. Pukanszky,Lecons sur les representations des Groupes, Dunod, Paris, 1967.
Mathematical Reviews (MathSciNet): MR36:311
[21a] P. Robba, Lemmes de Hensel pour les operateurs differentiels. Application a la reduction formelle des equations differentielles, Lnseignement Mathematique, Ser. II, 26 (1980), 279-311.
Mathematical Reviews (MathSciNet): MR82k:12022
Zentralblatt MATH: 0466.12014
[22] J. P. Serre, Corps Locaux (2nd Ed.),Hermann, Paris, 1968.
Mathematical Reviews (MathSciNet): MR50:7096
[23] J. P. Serre, Representations Lineaires des Groupes Finis (2nd Ed.),Hermann, Paris, 1971.
Mathematical Reviews (MathSciNet): MR50:4718
Zentralblatt MATH: 0205.04001
[24] T. A. Springer, and R. Steinberg, Conjugacy Classes in Lecture Notes in Mathe- matics, No. 131, Springer-Verlag Berlin, Heidelberg,1970.
Mathematical Reviews (MathSciNet): MR42:3091
[25] R. Steinberg, Lectures on Chevalley Groups, Dept. of Mathematics, Yale University, 1967.
Mathematical Reviews (MathSciNet): MR57:6215
[26] H. Turrittin, Convergent solutions of ordinary linear homogeneous equations in the neighborhood of an irregular singular point, Acta Math., 93 (1955),27-66.
Mathematical Reviews (MathSciNet): MR16:925a
Zentralblatt MATH: 0064.33603
[27] H. Turrittin, Reduction of ordinary differential equations to the Birkhoff canonical form, Trans. Amer. Math. So, 107 (1963), 485-507.
Mathematical Reviews (MathSciNet): MR27:368
Zentralblatt MATH: 0115.07002
[28] V. S. Varadarajan, On the ring of invariant polynomials on a semi-simple Lie algebra, Amer. J. Math., 90 (1968), 309-317.
Mathematical Reviews (MathSciNet): MR37:1529
Zentralblatt MATH: 0205.33303
[29] V. S. Varadarajan, Harmonic Analysis on Real Reductive Groups, Lecture Notes in Mathematics, No. 576, Springer-Verlag, Berlin, Heidelberg, 1977.
Mathematical Reviews (MathSciNet): MR57:12789
Zentralblatt MATH: 0354.43001
[30] V. S. Varadarajan, Lie Groups, Lie Algebras, and Their Representations, Prentice-Hall, En- glewood Cliffs, New Jersey, 1974.
Mathematical Reviews (MathSciNet): MR51:13113
Zentralblatt MATH: 0371.22001
[31] W. Wasow, Asymptotic Expansions for Ordinary Differential Equations, Interscience, New York, 1965.
Mathematical Reviews (MathSciNet): MR34:3041
Zentralblatt MATH: 0169.10903

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