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Olver P.J. — Equivalence, Invariants and Symmetry
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Название: Equivalence, Invariants and SymmetryАвтор: Olver P.J. Аннотация: 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.
Язык: Рубрика: Математика /Симметрия и группы /Статус предметного указателя: Готов указатель с номерами страниц ed2k: ed2k stats Год издания: 1995Количество страниц: 525Добавлена в каталог: 22.11.2004Операции: Положить на полку |
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Предметный указатель
Form, contact-invariant 235 Form, modified Maurer — Cartan 374 376 394 462 Form, row echelon 310 Forsyth, A.R. 211 214 384 [71] [72] Frame 17 67 253 390 Frame invariant 71 Frame moving 156 Frame, coordinate 252 Frame, eigen- 255 Frechet derivative 207 Frechet, R.M. 207 free 38 66 71 154 155 Free effectively 38 42 67 71 94 145 Free locally 38 42 58 94 Free particle 206 326 Free variable 351 394 Frobenius' Theorem 42 178 348 422 427 434 Frobenius, G. xii 421 [73] Fulling, S.A. 393 [74] Fully regular 178 266 268 271 Fully transverse 432 466 Function 24 78 112 Function affine 108 Function characteristic 131 429 Function classifying 262 267 371 436 Function differential 115 124 137 175 Function elliptic 102 198 Function generating 127 Function Hilbert 167 Function hypergeometric 102 199 Function invariant 66 68 109 Function linear fractional 156 195 205 Function potential 185 Function prolonged 112 121 123 Function scale-invariant 110 111 Function space 78 Function special 75 Function structure 257 261 347 433 Function symmetric 45 Function transformed 108 Function, rank of 12 Functional 222 235 285 337 342 Functionally dependent 12 26 267 Functionally independent 12 26 Functionally independent strictly 138 158 167 Functionally independent, differential invariants 137 239 Functionally independent, invariants 62 110 267 Fundamental differential invariant 147 153 157 161 162 171 193 202 Fundamental invariant 46 Fundamental multiplier 89 229 Fundamental multiplier representation 95 120 148 215 Fundamental representation 80 Fundamental solution 184 Fushchich, W.I. 173 [75] G-structure 289 305 G-valued equivalence problem 288 Gage, M. 251 [76] Galilean boost 184 Galileo, G. 184 Galois, E. 3 Gardner, R.B. 252 267 296 333 346 359 367 369 371 397 409 428 431 459 471 [28] [77—81] Gas dynamics 255 Gat, O. 205 [82] Gauge equivalent 83 88 212 319 Gauge factor 83 212 Gauge transformation 107 219 Gauss — Bonnet theorem 333 Gauss, C.F. 309 333 380 Gaussian curvature 174 272 380 384 385 Gaussian elimination 309 Gel’fand, I.M. 100 102 222 244 301 323 [83—85] General linear group 33 35 39 40 42 49 52 76 79 86 89 95 136 229 General relativity 394 Generalized symmetry 180 186 Generalized variational symmetry 244 Generalized vector field 119 Generate 410 Generating function 127 Generic integral element 468 Genuinely nonlinear 256 Geodesic 333 Geometric diffusion 247 Geometric object 1 Geometry xi Geometry affine 37 164 Geometry conformal 164 385 Geometry differential 377 421 Geometry Euclidean 381 Geometry extrinsic 380 Geometry hyperbolic 381 Geometry intrinsic 380 Geometry projective 164 211 Geometry spherical 381 Geometry symplectic 367 Geometry web 386 global 3 29 35 Global equivalence 441 Global invariant 45 Global isotropy subgroup 38 56 145 Goldschmidt, H.L. 244 397 409 428 430 431 459 471 [28] [86] Golubitsky, M. 11 61 [87] [88] Gonzadez-Lopez, A. 61 88 90 203 206 242 [89—97] Gonzalez-Gascon, F. 203 [89] Gotay, M. 244 246 345 [98] Goursat, E.J.-B. 430 Grace, J.H. 79 100 102 104 336 [99] Gradient 222 Graph 15 107 431 432 461 Graph prolonged 112 121 123 126 176 Graph, technique of the 431 461 Graustein, W.C. 381 383 [100] Gravity 83 Grayson, M. 251 [101] Green, M.L. 162 163 164 172 [102] Greene, C. 167 [103] Griffiths, P.A. 397 408 409 428 430 431 459 471 [28—30] Grissom, C. 407 [104] Groebner basis 279 Group 32 Group affine 37 39 41 50 59 66 72 88 94 134 136 157 174 250 269 276 364 Group classical 34 55 Group conformal 136 173 385 Group covering 54 441 Group Euclidean 37 67 71 155 156 164 173 250 299 378 Group general linear 33 35 39 40 42 49 52 76 79 86 89 95 136 229 Group Heisenberg 73 Group isometry 381 Group isotropy 38 40 58 139 140 163 295 Group Lie 32 48 53 54 254 268 435 441 Group one-parameter 36 42 55 107 117 429 Group orthogonal 34 43—45 54 55 73 282 291 302 387 389 393 Group Poincare 136 173 Group projective 39 57 59 155 181 241 250 Group prolonged 113 Group pseudo- 4 355 466 Group pseudo-orthogonal 39 282 393 Group quantum 102 Group quotient 38 67 145 Group rotation 34 43 80 108 114 134 137 158 172 174 192 239 377 Group similarity 141 157 250 Group structure 288 304 327 350 373 460 Group symplectic 34 39 54 55 134 282 Group topological 445 Group translation 59 88 Group unimodular see special linear group Group, global isotropy 38 56 145 Group, local Lie 53 444 Group, matrix Lie 33 54 72 76 288 Group, prolonged structure 395 Group, reduced structure 295 297 Group, special affine 37 134 155 157 174 241 250 Group, special linear 34 40 55 64 76 80 90 120 135 148 173 193 206 241 336 Group, special orthogonal see rotation group Group-invariant arc length 155 Group-invariant curvature 155 250 Guckenheimer, J. 20 [105] Guggenheimer, H.W. 37 155 156 157 174 380 381 [106] Guillemin, V. 11 [88] Guo, A. 191 [1] Gurevich, G.B. 97 100 102 104 [107] Gusein-Zade, S.M. 11 [14] Hadamard, J. 346 Halphen, G.-H. 136 211 [108] [109] Hamermesh, M. 75 82 [110] Hamilton, R.S. 251 [76] Hamilton, W.R. 31 60 Hamiltonian 31 102 Hamiltonian mechanics 31 34 60 126 127 221 Hamiltonian system 244 323 Hamiltonian system, multi- 272 367 Hausdorff space 8 Hausdorff, F. 8 Hawkins, T. 4 59 414 [111] Heat equation 182 185 210 Heat flow 386 Heisenberg group 73 Heisenberg, W. 73 Helmholtz equation 193 Helmholtz, H. 193 Heredero, R. 152 Hereman, W. 179 [44] [112] Herlt, E. 394 [141] Hermann, R. 422 [2] [3] [113] Hesse, L.O. 100 hessian 100 103 149 151 216 226 333 Hessian matrix 173 345 Hessian tensor 345 Higher order curvature tensor 392 Hilbert basis 103 335 Hilbert function 167 Hilbert's basis theorem 103 Hilbert's invariant integral 244 Hilbert, D. 79 100 103 167 244 335 429 430 447 448 [56] [114] [115] Hille, E. 151 195 199 403 [116] Hirota operator 100 Hirota, R. 100 Hodograph transformation 210 231 331 hole 29 Holm, D.D. 367 [59] Holmes, P. 20 [105] Holomorphic 8 Holonomic 222 Homogeneous 187 410 450 Homogeneous equation 188 Homogeneous polynomial 79 95 168 229 333 Homogeneous space 40 61 162 163 172 Homomorphism 33 56 120 Hopf — Cole transformation 185 Hopf — Rinow theorem 445 Hopf, E. 185 Hopf, H. 445 Horizontal 123 153 432 Horizontal component 123 124 156 Horizontal one-form 165 Hsu, L. 246 401 402 403 407 408 [30] [117] [118] Humphreys, J.E. 52 55 75 134 [119] Hyperbolic 255 Hyperbolic geometry 381 Hyperbolic partial differential equation 368 Hyperbolic space 393 Hyperbolic system 259 272 Hypergcometric function 102 199 Hyperplane 220 Ibragimov, N.H. 119 129 175 182 204 407 [11] [120—122] Icosahedral 199 Ideal 55 Ideal contact 416 Ideal derived 415 Ideal differential 414 428 430 447 Ideal exterior 410 414 Ideal polynomial 167 Identity 32 49 Identity Bianchi 393 Identity Jacobi 21 49 51 261 263 278 393 Identity tensor 391 Image processing 247 250 251 Immersed submanifold 13 Implicit function theorem 11 14 107 127 432 438 440 457 Implicit submanifold 16 Imprimitive 61 Ince, E.L. 195 198 [123] Independence condition 468 Independent finctionally 12 26 62 110 137 239 267 Independent linearly 25 218 Independent strictly 138 158 167 Independent variable 106 175 222 Indeterminancy, degree of 351 373 394 470 Indeterminate 394 Inductive method 328 Inequivalent Lagrangian 226 Inertia 43 Infinitesimal 20 412 Infinitesimal contact transformation 129 Infinitesimal generator 18 52 55 107 424 Infinitesimal invariance 65 92 110 141 179 236 237 Infinitesimal multiplier 85 87 92 247 Infinitesimal normalization 360 Infinitesimal representation 77 Infinitesimal symmetry condition 62 69 179 236 237 infinity 10 36 Inhomogeneous polynomial 81 100 209 333 Initial condition 413 Initial value problem 178 Integrability condition 178 186 354 Integrable 226 411 413 417 422 427 Integral curve 18 411 418 424 427 429 451 Integral element 412 427 456 467 470 Integral element generic 468 Integral element regular 455 Integral invariant 221 244 Integral submanifold 410 417 422 425 456 459 468 Integral submanifold maximal 424 Integral surface 411 452 458 Integrating factor 31 411 Integration by parts 224 243 Interior product 70 246 Internal symmetry 129 Intersection 14 Intransitive 61 153 193 202 355 366 461 471 Intransitive symmetry group 204 Intrinsic geometry 380 Intrinsic Method 358 Invariance equations 262 437 Invariant 2 44 46 62 91 109 110 258 424 Invariant absolute 91 Invariant coframe 71 155 157 Invariant combination 292 Invariant component 390 Invariant contact form 247 Invariant curvature 393 Invariant derived 260 262 437 Invariant differential equation 199 201 202 Invariant differential form 68 70 Invariant differential operator 147 153 157 165 171 Invariant evolution equation 249 Invariant foliation 61 Invariant frame 71 Invariant function 66 68 109 Invariant fundamental 46 Invariant global 45
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