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

$n^{th}$ order contact      112
Abelian      33 50 209 243 296 395 443
Ablowitz, M.J.      198 [43]
Abraham-Shrauner, B.      191 [1]
Absolute differential invariant      149
Absolute invariant      91
Absolute parallelism      253
Absorption      309 374 394 469
Absorption, equations      309 351 394
Ackerman, M.      [2] [3]
Adapted coframe      328
Adapted total derivative      316 324 340 400
Adjoint      218 219
Adjoint, representation      77 78
Adler, M.      102 [4]
Ado's Theorem      54
Ado, I.D.      54
Affine      51
Affine differential invariant      220
Affine function      108
Affine geometry      37 164
Affine group      37 39 41 50 59 66 72 88 94 134 136 157 174 250 269 276 364
Affine invariant arc length      339
Affine invariant curvature      251
Affine transformation      37
Airy equation      198
Airy, G.B.      198
Aitken, A.C.      43 [216]
Algebra abelian      51 54
Algebra computer      6 179 359
Algebra derived      55
Algebra differential      100
Algebra Virasoro      102
Algebra, symmetry      88
Algebraic function      359
Analytic      7 11 32 79 103 107 178 422 448
Analytic coframe      271 355
Anderson, I.M.      129 226 227 240 248 340 408 [5—10]
Anderson, R.L.      119 129 [11]
angle      137 140 148 192
Angular coordinate      41 42
Anti-symmetric      21 24 49 390
ARC      109 111
Arc length      155 157 241 250 301 333 339
Arc length, affine-invariant      339
Arc length, group-invariant      155
Arc parabolic      273
Area form      239
Arnol’d, V.I.      11 31 126 127 407 [12—14]
Associativity      32 443 445
Atlas      8
Augmented Hessian tensor      345
Automorphic form      102 198
Baecklund's Theorem      128 132 136 361 363 416
Baecklund, A.V.      119 128 129 136 [15]
Ball, J.M.      222 [16]
Bargmann, V.      82 [17]
Base coordinate      10
Base transformation      106
Basic contact form      122 123 130
Basic variable      351
Basis      51
Basis dual      253
Basis Groebner      279
Basis Hilbert      103 335
Beltrami, E.      383
Bianchi identity      393
Bianchi's Theorem      191
Bianchi, L.      191 [18]
Biform      296 346
BiHamiltonian system      366
Binary form      79 150 229 302 333
Binary form, symmetry group of      334
Binomial coefficient      112 167
Biquadratic      346
Bleecker, D.      83 [19]
Bluman, G.W.      110 175 186 187 190 209 211 [20—22] [144]
Bocharov, A.V.      407 408 [23]
Bonnet, O.P.      333
Boole, G.      95
Bott, R.      29 [24]
Boundary condition      222
Boundary layer      198
Boundary natural      198
Boundary value      178 225
Boussinesq equation      186 237
Boyer C.P.      394 [25]
Brachet, M.E.      20 [68]
Bracket Lie      21 23 28 49 51 69 78 120 257 417
Bracket Poisson      102
Bryant, R.L.      286 397 408 409 428 430 431 459 471 [26—30]
Buchberger, B.      279 [31]
Bundle cotangent      23 91 253
Bundle extended jet      106
Bundle jet      112 263
Bundle line      10
Bundle principal      305
Bundle tangent      17 84 91
Bundle vector      10 15 17 23 84 106
Burgers' equation      184 185
Burgers, J.      184
Calculus of variations      100 222 227 285 321
Canonical form      2 9 42 44 91 296
Canonical form rational      43
Canonical form, biforms      296
Canonical form, curvature tensors      393
Canonical form, differential operators      214
Canonical form, group orbits      42
Canonical form, Jordan      2 42 45
Canonical form, Laguerre — Forsyth      214
Canonical form, Lie algebras      59
Canonical form, maps      11
Canonical form, matrices      42 282 387
Canonical form, one-forms      30 281
Canonical form, ordinary differential equations      19 204
Canonical form, points      46
Canonical form, submanifolds      14
Canonical form, symbols      296
Canonical form, two-forms      31 43 281
Canonical form, vector fields      19 30
Canonical form, vectors      43
Canonical transformation      34 127
Caratheodory, C.      345 [32]
Cartan character      455 463 466
Cartan cquivalence method      4 206 304 358
Cartan form      244 246 286 329 345 357 358
Cartan structure equations      389
Cartan system      430 431
Cartan — Kaehler Theorem      178 348 373 409 415 456 470
Cartan — Kuranishi Theorem      397
Cartan's Lemma      26
Cartan's test      355 367 373 396 466 470
Cartan, E.      xii xiii 3-5 26 28 31 53 55 103 156 178 221 244 252 253 262 280 288 292 297 338 342 348 350 353 356 372 386 397 398 403 407 408 409 421 431 440 444 453 459 461 470 471 [33—42]
Cartesian product      10 15 37 46 61 254 305 425 431
Catastrophe theory      11
Cauchy characteristic      428
Cauchy data      448 456 458 459
Cauchy problem      178 448
Cauchy — Kovalevskaya Theorem      178 348 448 456 458
Cauchy, A.-L.      178 448
Cayley — Hamilton theorem      60
Cayley, A.      60 99
Center      54
Chain rule      23 114 116 128 212 277 436
Chakravarty, S.      198 [43]
Champagne, B.      179 [44]
Change of coordinates      8 18
Character Cartan      455 460 463 466
Character pseudo-      456 460
Character reduced      353 355 373 466—470

Characteristic      111 117 130 131 187 243
Characteristic Cauchy      428
Characteristic curve      246 429
Characteristic direction      168 428
Characteristic Euler      20
Characteristic form      119 179
Characteristic function      131
Characteristic polynomial      60
Characteristic speed      255
Characteristic strip      429
Characteristic system      62 428 430
Characteristic, method of      62 141 188
Chart      8
Chazy equation      198
Chazy, J.      198 199 [45]
Chern, S.-S.      333 397 408 409 428 430 431 459 471 [28] [46—50]
Chrastina, J.      338 [51]
Christoffel, E.B.      4 386 392 408 [52]
Churyumov, A.      61 [140]
Ciarlet, P.G.      100 [53]
circle      9 16 17 42 65 134 198 427
Clarkson, P.A.      xiii 61 198 199 [43] [54]
Classical field theory      244 345
Classical group      34 55
Classical invariant theory      xii 79 95 104 148—151 211 229 333 393 408
Classical mechanics      31
Classifying curve      272 318 327 332
Classifying function      262 267 371
Classifying manifold      266 268 271 367 396 435 437 441
Classifying manifold extended      277 302
Classifying manifold reduced      278 384
Classifying set      263 264
Classifying space      263 271 435
Classifying space extended      277
Classifying surface      272
Closed differential ideal      414 419 427 434
Closed form      29 31
Closed subgroup      33 40
Closure      414
Coboundary      88
Cocyle      88
Cohen, H.      102 [55]
Cohomology      29 88
Cole, J.D.      185
Coltame      253 288 297 390
Coltame adapted      328
Coltame contact-invariant      164 168 171 238
Coltame coordinate      252
Coltame covering      441
Coltame derivative      165 254 260 366 373 396 436 471
Coltame diagonalizing      282 378 385 387 391
Coltame eigen-      255
Coltame invariant      71 155 157
Coltame lifted      305 353 366 460
Coltame Maurer — Cartan      254 268 275 441
Coltame prolonged      375
Coltame regular      266 435 440
Coltame symmetry      256 259 272
Coltame, equivalence problem for      4 256 271 292 296 367 433 437
Coltame, G-invariant      71 156
Coltame, rank of      367
Coltame, symmetry group of      274 347 367 396
Commutativity      32 422 425
Commutator      21 49 55 77 86 166
Compact      77
Compact support      223
complete      445
COMPLEX      8 29
composition      22 27 113
Computer algebra      6 179 359
Computer vision      221 246
Conformal field theory      221
Conformal geometry      164 385
Conformal group      136 173 385
Conformal symmetry group      386
Conic section      205 220
conjugate      34 38
Conjugation      45 76 77
Connected      8 16 40 53 107 424
Connected component      33
Connected pathwise      16
Connected simply      16 54 441 443
Connection      4 263 387 389
Connection projective      398
Conservation law      186 242 244 329 345
Conservative      242
Constant type      295
Constraint      222
Contact      112 121
Contact conditions      130
Contact form      122 126 232 283 339 361 416 428 430
Contact form basic      122 123 130
Contact form invariant      247
Contact form pseudo-      339
Contact form quadratic      233
Contact ideal      416
Contact symmetry      180 251
Contact system      430 431
Contact transformation      126 128 129 230 361 416 429
Contact transformation group      134 152 176 242
Contact transformation infinitesimal      129
Contact transformation prolonged      128 416
Contact vector field      131 187 429
Contact-equivalent      228 230 342
Contact-invariant      153 238 300
Contact-invariant coframe      164 168 171 238
Contact-invariant form      235
Contact-invariant one-form      157 161 164
Contragredient      76 79
Control system      333
Convex      29 167 323
Coordinate angular      41 42
Coordinate base      10
Coordinate chart      8
Coordinate coframe      252 451 468
Coordinate differential form      25
Coordinate fiber      10
Coordinate frame      252
Coordinate local      32 252
Coordinate polar      41 239
Coordinate projective      100
Coordinate rectifying      19 42 63 187 243 423 426
Coordinate spherical      9 42
Coordinate, change of      8 18
Corank      427
Coset      34
Cotangent bundle      23 91 253
Cotangent space      23 71 252 253 390
Coullet, P.      20 [68]
Courant, R.      429 430 447 448 [56]
Covariant      98 101 102 333
Covariant derivative      323 339 389 391
Covariant differential      391
Covariant Jacobian      100 104 149
Covariant rational      334
Covering coframe      441
Covering group      54 441
Covering manifold      441
Covering map      12 54 271 441
Covering space      443
Cramer's rule      218
Cramer, G.      218
Crampin, M.      389 391 [57]
Cross product      219
Cross-ratio      46 97
Cubic curve      266
Cubic polynomial      97 104 335
Cummins, C.J.      393 [74]
Curvature      137 140 155 192
Curvature affine-invariant      251

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