Equivalence, Invariants and Symmetry

Erscheinungsjahr 2008
ISBN: 978-0-521-47811-3
Verlag: Cambridge University Press

Buch, Englisch, 544 Seiten, Format (B × H): 157 mm x 235 mm, Gewicht: 1024 g

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.

Autoren/Hrsg.

Olver, P.

Olver, Peter J.

Fachgebiete

• Mathematik | Informatik Mathematik Mathematische Analysis
• Mathematik | Informatik Mathematik Geometrie

Inhaltsverzeichnis

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.