Equivalence, Invariants and Symmetry

Presents an innovative synthesis of methods used to study problems of equivalence and symmetry.

Peter J. Olver (Author)

9780521478113, Cambridge University Press

Hardback, published 30 June 1995

544 pages, 6 b/w illus. 7 tables 147 exercises
22.9 x 15.2 x 3.5 cm, 0.86 kg

'The book should be warmly recommended to graduate students of mathematics and mathematical physics.' European Mathematical Society Newsletter

Drawing on a wide range of mathematical disciplines, including geometry, analysis, applied mathematics and algebra, this book presents an innovative synthesis of methods used to study problems of equivalence and symmetry which arise in a variety of mathematical fields and physical applications. Systematic and constructive methods for solving equivalence problems and calculating symmetries are developed and applied to a wide variety of mathematical systems, including differential equations, variational problems, manifolds, Riemannian metrics, polynomials and differential operators. Particular emphasis is given to the construction and classification of invariants, and to the reductions of complicated objects to simple canonical forms. This book will be a valuable resource for students and researchers in geometry, analysis, algebra, mathematical physics and other related fields.

1. Geometric foundations
2. Lie groups
3. Representation theory
4. Jets and contact transformations
5. Differential invariants
6. Symmetries of differential equations
7. Symmetries of variational problems
8. Equivalence of coframes
9. Formulation of equivalence problems
10. Cartan's equivalence method
11. Involution
12. Prolongation of equivalence problems
13. Differential systems
14. Frobenius' theorem
15. The Cartan–Kahler existence theorem.

Subject Areas: Geometry [PBM]