Olver P.J. — Equivalence, Invariants and Symmetry :: Электронная библиотека попечительского совета мехмата МГУ

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Olver P.J. — Equivalence, Invariants and Symmetry

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Название: Equivalence, Invariants and Symmetry

Автор: 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: 1995

Количество страниц: 525

Добавлена в каталог: 22.11.2004

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID

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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