Equivalence, Invariants and Symmetry
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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J 198 43
Jets and Contact Transformations
Bäcklund A V 119 128 129 136
Symmetries of Differential Equations
Bocharov A V 407 408 23
Prolongation of Equivalence Problems
The CartanKähler Existence Theorem
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According action acts apply associated basic Cartan Chapter classifying coefficients coframe complete compute connected Consider constant contact form contact transformation coordinates corresponding curve defined Definition denote dependent derivative determine differential invariants differential operators dimension discussed element equivalence problem essential Example Exercise existence fact formula function fundamental given group action group G group parameters hence ideal identity implies important independent infinitesimal integral integral submanifold Lagrangian Lie algebra Lie group linear locally manifold matrix meaning method multiplier normalize Note one-forms orbit order differential ordinary differential equation original particular point transformation projective prolonged proof Proposition Prove rank reduced regular representation restrict result satisfy second order smooth solution space structure structure equations subgroup subset symmetry group tangent tangent vectors Theorem theory tion torsion transformation vanish variables vector field