Differential Galois Theory and Non-Integrability of Hamiltonian Systems
- - - The book is an excellent introduction to non-integrability methods in Hamiltonian mechanics and brings the reader to the forefront of research in the area. The inclusion of a large number of worked-out examples, many of wideapplied interest, is commendable. There are many historical references...
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| Format: | eBook |
| Language: | English |
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Basel
Birkhäuser
1999, 1999
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| Edition: | 1st ed. 1999 |
| Series: | Modern Birkhäuser Classics
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| Subjects: | |
| Online Access: | |
| Collection: | Springer Book Archives -2004 - Collection details see MPG.ReNa |
Table of Contents:
- 1 Introduction
- 2 Differential Galois Theory
- 2.1 Algebraic groups
- 2.2 Classical approach
- 2.3 Meromorphic connections
- 2.4 The Tannakian approach
- 2.5 Stokes multipliers
- 2.6 Coverings and differential Galois groups
- 2.7 Kovacic’s algorithm
- 2.8 Examples
- 3 Hamiltonian Systems
- 3.1 Definitions
- 3.2 Complete integrability
- 3.3 Three non-integrability theorems
- 3.4 Some properties of Poisson algebras
- 4 Non-integrability Theorems
- 4.1 Variational equations
- 4.2 Main results
- 4.3 Examples
- 5 Three Models
- 5.1 Homogeneous potentials
- 5.2 The Bianchi IX cosmological model
- 5.3 Sitnikov’s Three-Body Problem
- 6 An Application of the Lamé Equation
- 6.1 Computation of the potentials
- 6.2 Non-integrability criterion
- 6.3 Examples
- 6.4 The homogeneous Hénon-Heiles potential
- 7 A Connection with Chaotic Dynamics
- 7.1 Grotta-Ragazzo interpretation of Lerman’s theorem
- 7.2 Differential Galois approach
- 7.3 Example
- 8 Complementary Results and Conjectures
- 8.1 Two additional applications
- 8.2 A conjecture about the dynamic
- 8.3 Higher-order variational equations
- A Meromorphic Bundles
- B Galois Groups and Finite Coverings
- C Connections with Structure Group