Available in electronic format
Available in print format
Bulletin of the American Mathematical Society
Bulletin of the American Mathematical Society
ISSN 1088-9485(e) ISSN 0273-0979(p)
     

Book Review

The AMS does not provide abstracts of book reviews. You may download the entire review from the links below.

Retrieve article in: PDF

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

2.
Y. André, Différentielles non commutatives et théorie de Galois différentielle ou aux différences, Ann. Scient. Éc. Nor. Sup. 34 (2001) 685-739. MR 2002k:12013

3.
D. Bertrand, Théorie de Galois différentielle, Cours de DEA, Université de Paris VI, 1986.

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

5.
D. Bertrand, Review of the book Lectures on Differential Galois Theory by A. Magid, Bulletin of the Amer. Math. Soc. (N.S.) 33 (1996) 289-294.

6.
A.A. Bolibrukh, The Riemann-Hilbert problem, Russian Math. Surveys 45 (2) (1990) 1-47. MR 92j:14014

7.
F. Beukers, D. Brownawell, G. Heckman, Siegel normality, Ann. of Math. 127 (1988) 279-308. MR 90e:11106

8.
A. Buium, Differential Function Fields and Moduli of Algebraic Varieties, Lectures Notes in Math. 1226. Springer-Verlag, Berlin, 1986. MR 88e:14010

9.
C. Chevalley, Théorie des groupes de Lie, Hermann, Paris, 1951. MR 14:448d

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

13.
N.M. Katz, On the calculation of some differential Galois groups, Invent. Math. 87 (1987) 13-61. MR 88c:12010

14.
E. Kolchin, Differential algebra and algebraic groups. Academic Press, New York, 1973. MR 58:27929

15.
M. Loday-Richaud, Stokes phenomenon, multisummability and differential Galois groups, Ann. Inst. Fourier 44 (1994), 849-906. MR 95g:34010

16.
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

27.
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

28.
M.E. Vessiot, Sur l'intégration des équations différentielles linéaires, Ann. Sci. École Norm. Sup. (3) 9 (1892) 197-280.

29.
W. Wasow, Asymptotic Expansions for Ordinary Differential Equations. Dover, New York, 1987. MR 88i:34003


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


  AMS Website Logo Small Comments: webmaster@ams.org
© Copyright 2009, American Mathematical Society
Privacy Statement
Search the AMSPowered by Google