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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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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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