Equivalence, Invariants and Symmetry

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Cambridge University Press, 30.06.1995 - 525 Seiten
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.
 

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Inhalt

Introduction
1
Geometric Foundations
7
Lie Groups
32
Representation Theory
75
Jets and Contact Transformations
105
Differential Invariants
136
Symmetries of Differential Equations
175
2
198
Cartans Equivalence Method
304
Involution
347
Prolongation of Equivalence Problems
372
Anderson R L 119 129 11
407
Differential Systems
409
Frobenius Theorem
421
The CartanKahler Existence Theorem
447
Tables
472

Aitken A C 43 216
216
Symmetries of Variational Problems
221
M 129 226 227 240
226
Equivalence of Coframes
252
Formulation of Equivalence Problems
280

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