Galois Theory of Linear Differential Equations

Cover......Page 1
ISBN......Page 5
Preface......Page 8
Contents......Page 16
Algebraic Theory......Page 22
1 Picard-Vessiot Theory......Page 24
2 Differential Operators and Differential Modules......Page 60
3 Formal Local Theory......Page 84
4 Algorithmic Considerations......Page 126
Analytic Theory......Page 168
5 Monodromy, the Riemann-Hilbert Problem and the Differential Galois Group......Page 170
6 Differential Euqations on the Complex Sphere anf the Riemann-Hilbert Problem......Page 184
7 Exact Asymptotics......Page 214
8 Stokes Phenomenon and Differential Galois Groups......Page 258
9 Stokes Matrices and Meromorphic Classification......Page 274
10 Universal Picard-Vessiot Rings and Galois Groups......Page 290
11 Inverse Problems......Page 302
12 Moduli for Singular Differential Equations......Page 326
13 Positive Characteristic......Page 348
Appendices......Page 368
A Algebraic Geometry......Page 370
B Tannakian Categories......Page 406
C Sheaves and Cohomology......Page 424
D Partial Differential Equations......Page 444
Bibliography......Page 454
List of Notations......Page 476
Index......Page 479
Back cover......Page 484