內容簡介
線性微分方程的伽羅瓦理論《國外數學名著系列33:線性微分方程的伽羅瓦理論》專門論述線性微分方程的伽羅瓦理論，涉及諸多方面：代數理論（尤其是微分伽羅瓦理論）、形式理論、分類、有限項可解性判定算法、單值性、希爾伯特21問題、漸近性和可求和性，反問題以及具正特徵值的線性微分方程。附錄是本書所用到的代數幾何、線性代數群、層及Tannakian範疇中的一些概念。
作者簡介
作者:(荷)范德帕特(VanderPut、M.)等
目錄
Algebraic Theory
1 Picard Vessiot Theory
1.1 Differential Rings and Fidlds
1.2 Linear Differential Eqations
1.3 Picard-Vessiot Extensions
1.4 The Differential Galois Group
1.5 Liouvillian Extensions
2 Differential Operatiors and Differential Modules
2.1 The Ring=k of Differential Operatiors
2.2 Constuctions with Differential Modules
2.3 Constuctions with Differential Operatiors
2.4 Differential Modules and Representations
3 Formal Local Theory
3.1 Formal Classification of Differential Equations
3.2 The Universal Picalr-Vessiot Ring of K
3.3 Newton Polygons
4 Algorithimc Considerations
4.1 Rational and Exponential Solutions
4.2 Factoring Linear Operatiors
4.3 Liouvillinan Solutions
4.4 Finnite Differential Galois Groups
Analytic Theory
5 Monodromy,the Riemann-Hilbert Problem,and the Differential Galois Group
6 Differential Equations on the Complex Sphere and the Rimann-Hillbert Problem
7 Exact Asymptotics
8 Stokes Phenmenon and Differential Galois Groups
9 Stookesmatricesand Meromorphic Classification
10 Universal Picard-Vessiot Rings and Galois Groups
11 Inverse Problems
12 Modeli for Singular Differential Equations
13 Positive Characteristic
Appendices
A Algebraic Geometry
B Tannakian Categories
Csheavesand Cohmology
D Partial Differential Equations
Bibliography
List of Notiation
Index
