Equivalence, Invariants and Symmetry
Equivalence, Invariants and Symmetry
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This book presents an innovative synthesis of methods used to study the problems of equivalence and symmetry that arise in a variety of mathematical fields and physical applications. It draws on a wide range of disciplines, including geometry, analysis, applied mathematics, and algebra. Dr. Olver develops systematic and constructive methods for solving equivalence problems and calculating symmetries, and applies them to a variety of mathematical systems, including differential equations, variational problems, manifolds, Riemannian metrics, polynomials, and differential operators. He emphasizes the construction and classification of invariants and 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 related fields.
- Includes numerous exercises and historical details
- Theory is illustrated by many examples and applications
- Style is not overly technical
Reviews & endorsements
"...represents an important effort to present the theory of the equivalence problem in a modern language with many new applications to concrete situations; in the author's words, 'it is a provocative blend of mathematical flavors'. Most of the material is of interest, and easily readable, for a wide class of specialists in different areas, as the book offers applications ranging over a great variety of fields." Jaime Muñoz Masqué, Mathematical Reviews
"Olver's highly original exposition gives a unified approach to a wide variety of problems of this sort via Cartan's equivalence method....this well-written book will interest a wide variety of mathematicians and graduate students." D.V. Feldman, Choice
Product details
February 2009Paperback
9780521101042
544 pages
229 × 152 × 31 mm
0.79kg
6 b/w illus. 7 tables 147 exercises
Available
Table of Contents
- 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.
