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

singular      3
Singular orbit      44 98
Singular variety      200
Singularity differential form      30 31 365 427
Singularity differential system      455
Singularity Lagrangian      225 301 322 323
Singularity map      11
Singularity submanifold      14
Singularity vector field      19
Skew-adjoint      218
Skew-symmetric matrix      34 39 43 54 73 76
Slice      42 47 275 423 430
Smooth      7 10 32 79 103 107 113 178 222 422
Sokolov, V.V.      134 152 186 206 246 407 408 [23] [168] [205] [212]
Solitary wave      186
Soliton      100 102 180 186 246
Solution      39 107 176
Solution fundamental      184
Solution invariant      187
Solution similarity      110
solvable      191 193 241
Space classifying      263 271 435
Space cotangent      23 71 252 253 390
Space covering      443
Space dynamical      247
Space Euclidean      7 29 33 37 106 164 277 393
Space extended      84
Space function      78
Space Hausdorff      8
Space homogeneous      40 61 162 163 172
Space hyperbolic      393
Space jet      112 121 139 175 222
Space parameter      13 28
Space projective      9 36 39 41 218
Space prolonged      375
Space quotient      34
Space tangent      17 20 22 58 253 390 412
Space tensor      76
Space topological      7
Space total      106 112 222
Space vector      23
Space vertical      112
Space, translationally invariant      60
Space-time manifold      394
Special affine group      37 134 155 157 174 241 250
Special function      75
Special linear group      34 40 55 64 76 80 90 120 135 148 173 193 206 241 336
Special orthogonal group      see rotation group
Sphere      9 16 17 23 40 41 42 44 393
Spherical coordinates      9 42
Spherical geometry      381
Spiral      42
Spivak, M.      20 21 [206]
Stabilization      141 269 436
Stabilization pseudo-      142 153 162 170 172 193 202
Stabilization, order of      141 154 161 165 171 200 247
Stable orbit dimension      141 143
Standard equivalence problem      227 285 321
Stephani, H.      394 [141]
Stereographic projection      9
Sternberg, S.      31 244 289 305 356 [86] [204] [207]
Strang, G.      309 [208]
Strictly independent      138 158 167
Strictly overlap      16 271
String theory      221
Stroh, E.      103 [209]
Strong ellipticity      346
Structure constant      51 72 261 424 433 435
Structure equations      72 257 306 350 359 373 433
Structure equations Cartan      389
Structure function      257 261 347 433
Structure group      288 304 327 350 373 460
Structure group prolonged      395
Structure group reduced      295 297
Structure invariant      262 267 296 299 328 359 396 436 471
Structure map      263 266 270 367
Structure map extended      277
Struik, D.J.      381 [210]
Sturmfels, B.      102 103 [211]
Subalgebra      53
Subgroup      33 40
Subgroup closed      33 40
Subgroup derived      55
Subgroup discrete      35 54 102
Subgroup global isotropy      38 56 145
Subgroup isotropy      37 38 40 58 139 140 163 295
Subgroup Lie      33 53
Subgroup normalize      55 190
Subgroup one-parameter      52 53
Submanifold      13 28 33 107 172 438
Submanifold immersed      13
Submanifold implicit      16
Submanifold integral      410 417 422 424 425 456 459 468
Submanifold invariant      47 64
Submanifold parametrized      13 279
Submanifold regular      14
Submanifold self-intersecting      14
Submanifold, canonical form for      14
Submanifold, equivalence problem for      14
Submanifold, singularity of      14
Submaximal symmetry group      205 242
subspace      77
Super derivation      27
Super-symmetric      26
surface      172 264 333 380 411
Surface classifying      272
Surface integral      411 452 458
Surface invariant conditions      110
Surface Landsberg      333
Surface of revolution      383
Svinolupov, S.I.      134 407 408 [23] [212]
Sylvester's theorem      43
Sylvester, J.J.      43
Symbol      168 170 296 346
Symbolic method      100 408
symmetric      112 168
Symmetric function      45
Symmetric matrix      43 44 282 387
Symmetric multi-index      112 223
Symmetric power      80
Symmetric super-      26
Symmetry      38 177 178
Symmetry contact      180 251
Symmetry fiber-preserving      176
Symmetry generalized      180 186 244
Symmetry group      1 39 65
Symmetry group conformal      386
Symmetry group discrete      199 275
Symmetry group infinitesimal      62 69 179 236 237
Symmetry group intransitive      204
Symmetry group of binary form      334
Symmetry group of coframe      274 347 367 396
Symmetry group of differential equation      136 179 185 191
Symmetry group of Euler — Lagrange equation      236 238 240
Symmetry group of ordinary differential equation      180 187— 400—403 406 407
Symmetry group of partial differential equation      182—187
Symmetry group of Riemannian metric      392
Symmetry group of system of equations      65
Symmetry group submaximal      205 242
Symmetry internal      129
Symmetry point      176 203
Symmetry potential      186
Symmetry reduction      187 190 203
Symmetry variational      235 244 246 345
Symmetry, algebra      88
Symmetry, coframe      256 259 272
Symmetry, divergence      237 242
Symplectic      31 127 176 291
Symplectic form      34
Symplectic geometry      367

Symplectic group      34 39 54 55 134 282
Syzygy      103 104 171 174 335
Takhtajan, L.A.      198 [213]
Tangent bundle      17 84 91
Tangent space      17 20 22 58 253 390 412
Tangent vector      17 22 432
Tannenbaum, A.      xiii 155 247 249 251 [189] [190] [201]
Taylor polynomial      112 113
Taylor series      248
Taylor, B.      112 248
Technique of the graph      431
Tensor bundle      390
Tensor curvature      4 389 391 392 393
Tensor field      390
Tensor Hessian      345
Tensor identity      391
Tensor metric      387
Tensor product      76
Tensor representation      80
Tensor Ricci      393
Tensor space      76
Tensor Weyl      393
Tetrahedral      199
TeX      xv
Theorem Ado's      54
Theorem Baecklund's      128 132 136 361 363 416
Theorem Bianchi's      191
Theorem Cartan — Kaehler      178 348 373 409 415 456 470
Theorem Cartan — Kuranishi      397
Theorem Darboux'      30 268 281 364 366 416
Theorem Divergence      224 225
Theorem Egregium      380
Theorem Frobenius'      42 178 348 422 427 434
Theorem Gauss — Bonnet      333
Theorem Hilbert's Basis      103
Theorem Hopf — Rinow      445
Theorem Implicit Function      11 14 107 127 432 438 440 457
Theorem Inverse Function      12 275 423
Theorem Kruskal — Katona      167
Theorem Macaulay's      167 169
Theorem Noether's      221 244 246
Theorem Second Fundamental      103
Theorem Sylvester's      43
Theorem Third Fundamental      444
Theorem, First Fundamental      102
Third Fundamental Theorem      444
Thompson, G.      226 227 407 [10] [lO4]
Tirapegui, E.      20 [68]
Topological group      445
Topological space      7
topology      8 14 29
Torsion      306 308 355 374 396 471
Torus      15 41 45
Total derivative      115 124 223 232
Total derivative adapted      316 324 340 400
Total derivative truncated      130 338
Total derivative, higher order      116
Total differential      124 153 157 165 232
Total divergence      225 236
Total Jacobian determinant      166
Total Jacobian matrix      166 230 235
Total Jacobian multiplier      165
Total Jacobian polynomial      226
Total space      106 112 222
Trace      45
Trallsitive      40 44 58 61 135 155 200 295 355 359 461
Trallsitive locally      67
Transcendent      403 407
transform      100
Transformation affine      37
Transformation base      106
Transformation canonical      34 127
Transformation contact      126 128 129 230 361 416 429
Transformation fiber-preserving      106 227 321
Transformation gauge      107 219
Transformation group      5 35 44 55 136 424
Transformation group contact      134 152 176 242
Transformation group local      35
Transformation group point      58 135 152
Transformation group regular      41 42 46 110
Transformation hodograph      210 231
Transformation Hopf — Cole      185
Transformation infinitesimal contact      129
Transformation Legendre      126 127 323
Transformation linear      33
Transformation linear fractional      36 46 81 114 148 181
Transformation Moebius      36
Transformation orientation-preserving      33 377
Transformation orientation-reversing      331 377
Transformation point      106 128 284
Transformation prolonged      113 128 416
Transformation volume-preserving      37 70 176 250 281 336
Transformed function      108
Translation      19 37 57 88
Translation group      59 88
Translationally invariant      60 64
Transvectant      99 100 101 149 199 216 219
Transvectant equation      102
Transvectant partial      103
Transverse      67 107 109 123 126 461 470
Transverse fully      432 466
Tresse, M.A.      4 136 146 166 397 407 408 [214] [215]
triangle      199 443
Trivial multiplier      83
Trivial multiplier representation      88
Trivial symmetry      188
Truncated total derivative      130 338
Truncated total differential      125
Tu, L.W.      29 [24]
Turnbull, H.W.      43 [216]
Two-form      31 43 281 369
Two-form nonclosed      31 367
Two-form, equivalence problem for      31 281 291 367
Two-form, rank of      31 43 281
TYPE      390
Type constant      295
Type nonconstant      294 306 350 471
Underdetermined      287 297 448
Underdetermined Kovalevskaya form      448 458
Unimodular      34
Unimodular group      see special linear group
Ushveridze, A.G.      88 [217]
Varchenko, A.N.      11 [14]
Variable basic      351
Variable dependent      106 175 222
Variable free      351 394
Variable independent      106 175 222
Variation      223 248
Variation of parameters      195
Variational derivative      223
Variational problem      222 230 235 285 321 337 342
Variational problem Dirichlet      240
Variational problem Newtonian      225
Variational problem, equivalence problem for      227 285
Variational symmetry      235 246 345
Variational symmetry generalized      244
Variational symmetry group      236 238 240 242 245 332
Variety      16 24 39 176 412
Variety determinantal      278
Variety regular      16 412 438
Variety singular      200
Vassiliou, P.      408 [218]
Vector bundle      10 15 17 23 84 106
Vector field      17 20 23 36 55 69 84 107 117 253 369
Vector field contact      131 187 429
Vector field evolutionary      119
Vector field generalized      119
Vector field invariant      48 66 67 92 94
Vector field prolonged      117
Vector field system      408 416 421 427 428

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