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Book Review
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Book Information
Author(s):
Marius van der Put and Michael Singer
Title:
Galois theory of linear differential equations
Additional book information:
Springer-Verlag,
Berlin,
2003,
xviii+438,
$99.00,
ISBN 3-540-44228-6
References:
-
- 1.
- Y. André, Quatre descriptions des groupes de Galois différentiels, Sém. Algèbre Paris 86-87, Lecture Notes in Math. 1296 Springer, 1987, 28-41. MR 89e:12012
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- 3.
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- 4.
- D. Bertrand, Groupes Algebriques et equations differentielles lineaires, Séminaire Bourbaki, 44ème année, 1991/92, Astérisque No. 206 (1992), Exp. No. 750, 4, 183-204. MR 94b:34006
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- 10.
- P. Deligne, Catégories tannakiennes. The Grothendieck Festschrift, vol. II. Progress in Math. 87. Birkhäuser, Boston, 1990, 111-196. MR 92d:14002
- 11.
- I. Kaplansky, An Introduction to Differential Algebra. Hermann, Paris, 1976. MR 57:297
- 12.
- N.M. Katz, A conjecture in the arithmetic theory of differential equations. Bull. Soc. Math. France 110 (1982) 203-239. MR 84h:14014a
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- B. Malgrange, Le groupoïde de Galois d'une feuilletage, Monographie de l'Enseignement Mathémathique 38 (2001) 465-501. MR 2004a:58027
- 17.
- B. Malgrange, On Nonlinear Differential Galois Theory, Chin. Ann. of Math. 23B:2 (2002) 219-226. MR 2003g:32051
- 18.
- J. Martinet, J.P. Ramis, Théorie de Galois différentielle et resommation. In Computer Algebra and Differential Equations, E. Tournier ed. Academic Press, London, 1989, 117-214. MR 91d:12014
- 19.
- J.J. Morales-Ruiz, Differential Galois Theory and Non-Integrability of Hamiltonian systems, Progress in Mathematics 179, Birkhäuser, Basel, 1999. MR 2000g:37076
- 20.
- E. Picard, Sur les groupes de transformation des équations différentielles linéaires, C.R. Acad. Sci. Paris 96 (1883) 1131-1134.
- 21.
- E. Picard, Sur équations différentielles et les groupes algébriques des transformations, Ann. Fac. Sci. Univ. de Toulouse (1) 1 (1887), A1-A15.
- 22.
- E. Picard, Traité d'Analyse, Tome III, Gauthiers-Villars, Paris, 1928.
- 23.
- J. Plemelj, Problems in the sense of Riemann and Klein, Interscience Publishers, New York, 1964. MR 30:5008
- 24.
- M. van der Put, Recent work on differential Galois theory, Séminaire Bourbaki, 50ànnée, 1997-98, Astérisque No. 252 (1998), Exp. No. 849, 5, 341-367. MR 2000h:12010
- 25.
- M. Singer, Direct and Inverse Problems in Differential Galois Theory. In Cassidy, Bass, Buium, eds., Selected Works of Ellis Kochin with Commentary, pp. 527-554, AMS, 1999. MR 2000g:01042
- 26.
- H. Umemura, Differential Galois theory of infinite dimension, Nagoya Math. J. 144 (1996) 59-135. MR 98c:12010
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- V.S. Varadarajan, Linear Meromorphic differential equations: a modern point of view, Bulletin of the Amer. Math. Soc. (N.S.) 33 (1996) 1-42. MR 96h:34011
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Additional Information:
Reviewer(s):
Juan
J.
Morales-Ruiz
Affiliation:
University Politecnica de Catalunya
Email:
juan.morales-ruiz@upc.es
Review Information:
Journal:
Bull. Amer. Math. Soc.
41
(2004),
351-356.
MSC
(2000):
Primary 12H05, 34M15, 34M50;
Secondary 13N10, 34A25, 34A05, 34A30, 34M05, 34M25, 34M30, 34M35, 34M37, 34M40, 34M45
PII:
S 0273-0979(04)01010-9
Posted:
March 12, 2004
Copyright of article:
Copyright
2004,
American Mathematical Society
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