等值、不变量和对称性 英文版
作者：（美）皮特.奥立弗 著
出版时间：2018年版
目录
Preface
Acknowledgments
Introduction
1. Geometric Foundations
Manifolds
Functions
Submanifolds
Vector Fields
Lie Brackets
The Differential
Differential Forms
Equivalence of Differential Forms
2. Lie Groups
Transformation Groups
Invariant Subsets and Equations
Canonical Forms
Invariant Functions
Lie Algebras
Structure Constants
The Exponential Map
Subgroups and Subalgebras
Infinitesimal Group Actions
Classification of Group Actions
Infinitesimal Invariance
Invariant Vector Fields
Lie Derivatives and Invariant Differential Forms
The Maurer-Cartan Forms
3. Representation Theory
Representations
Representations on Function Spaces
Multiplier Representations
Infinitesimal Multipliers
Relative Invariants
Classical Invariant Theory
4. Jets and Contact Transformations
Transformations and Functions
Invariant Functions
Jets and Prolongations
Total Derivatives
Prolongation of Vector Fields
Contact Forms
Contact Transformations
Infinitesimal Contact Transformations
Classification of Groups of Contact Transformations
5. Differential Invariants
Differential Invariants
Dimensional Considerations
Infinitesimal Methods
Stabilization and Effectiveness
Invariant Differential Operators