Equivalence, Invariants and SymmetryCambridge University Press, 30.06.1995 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. |
Inhalt
| 1 | |
| 7 | |
Lie Groups | 32 |
Representation Theory | 75 |
Jets and Contact Transformations | 105 |
Differential Invariants | 136 |
Symmetries of Differential Equations | 175 |
Symmetries of Variational Problems | 221 |
Involution | 347 |
Prolongation of Equivalence Problems | 372 |
Differential Systems | 409 |
Frobenius Theorem | 421 |
The CartanKähler Existence Theorem | 447 |
Tables | 472 |
| 477 | |
Symbol Index | 490 |
Equivalence of Coframes | 252 |
Formulation of Equivalence Problems | 280 |
Cartans Equivalence Method | 304 |
Author Index | 499 |
| 504 | |
Häufige Begriffe und Wortgruppen
associated canonical form Cartan form change of variables classifying manifolds coframe derivatives compute constant contact form contact transformation contact-invariant coordinates covariants defined Definition denote dependent variables derived invariants differential forms differential invariants differential operators differential system equivalence problem Euler–Lagrange equation Example Exercise fiber-preserving finite-dimensional formula G-invariant GL(n group action group parameters hence implies infinitesimal integral element integral submanifold invariant coframe invariant differential involutive jet space Lagrangian Lie algebra Lie bracket lifted coframe linear matrix Maurer–Cartan forms multiplier representation normalize one-forms open subset orbit dimension order differential invariants order ordinary differential ordinary differential equation partial differential equations point transformation polynomial prolonged proof rank relative invariant satisfy scalar smooth solution structure equations structure functions structure group structure invariants subgroup symmetry group tangent vectors Theorem tion torsion coefficients transformation group two-forms vanish variational problem vector field vector field system