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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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Invariant integral 221 Invariant joint 47 Invariant local 45 Invariant locally 64 Invariant one-form 92 146 Invariant relative 91 92 93 95 109 247 249 425 Invariant solution 187 Invariant structure 262 267 296 299 328 359 396 436 471 Invariant submanifold 47 64 Invariant subset 40 44 47 Invariant subspace 77 Invariant surface conditions 110 Invariant system 64 Invariant translationally 60 64 Invariant vector field 48 66 67 92 94 Invariant volume form 71 Invariant, functionally independent 62 110 Inverse 32 35 Inverse function theorem 12 275 423 Inverse problem 227 inversion 20 37 50 57 68 81 184 Involutive 355 367 417 419 422 468 470 Ioss, G. 20 [68] Irrational flow 41 44 45 Irreducible 77 78 Irreducible representation 80 Isometric 386 392 Isometric equivalence 299 320 377 Isometry 37 282 299 377 Isometry group 381 393 Isotropy subgroup 37 38 40 58 139 140 163 295 Isotropy subgroup global 38 56 145 Jacobi identity 21 49 51 261 263 278 393 Jacobi, C.G.J. 11 21 Jacobian covariant 100 104 149 Jacobian determinant 25 27 100 Jacobian determinant total 166 Jacobian differential operator 150 Jacobian matrix 11 22 26 176 423 438 Jacobian matrix total 166 230 235 Jacobian matrix, top order 139 Jacobian multiplier representation 84 92 Jacobian multiplier representation total 165 Jacobian polynomial 226 Jacobson, N. 54 88 [124] Janenko, N.N. 255 [200] jet 112 292 Jet bundle 112 263 Jet extended bundle 106 Jet prolongation 112 121 123 176 Jet space 112 121 139 175 222 Joint invariant 47 Jordan canonical form 2 42 45 Jordan, C. 2 42 45 Kaehler, E. xii 178 348 Kalnins, E.G. 209 [125] [126] Kamran, N. xiii 61 88 90 129 246 267 286 287 311 321 323 338 339 340 342 358 368 401 402 403 407 408 428 [s] [9] [79] [94—97] [117] [118] [127—135] Karlgede, A. 394 [136] [137] Katona, G.O.H. 167 Kernel 206 Killing, W. 55 kinetic energy 225 King, R.C. 393 [74] Klein, F. 37 Kleitman, D.J. 167 [103] Klimyk, A.U. 75 [220] Kobayashi, S. 393 [138] Komrakov, B. 61 [139] [140] Korteweg — deVrics equation 187 238 Korteweg, D.J. 187 238 Kovalevskaya form 448 459 Kovalevskaya, S. 178 448 Kramer, D. 394 [141] Kraunse, J. 204 [142] Kreysig, E. 387 [143] Kronecker delta 24 131 343 391 392 Kronecker, L. 24 131 Kruskal — Katona Theorem 167 Kruskal, J. 167 Kumei, S. 110 175 186 187 190 209 211 [20—22] [144] Kuranishi, M. 356 397 [145—147] Lagrange, J. L. 222 223 Lagrangian 222 230 240 285 342 Lagrangian form 222 230 233 285 342 Lagrangian inequivalent 226 Lagrangian nondegenerate 225 227 323 Lagrangian null 225 234 Lagrangian quadratic 241 346 Lagrangian, equivalence problem for 227 285 290 321 328 337 342 357 Lagrangian, singularity of 225 301 323 Laguerre — Forsyth normal form 214 Laguerre, E. 211 214 [148] Lamb, K.G. 403 [128] Lame equation 198 Lame, G. 198 Landsberg surface 333 Landsberg, G. 333 Laplace equation 115 240 Laplace — Beitrami operator 383 Laplace, P.S. 115 318 383 Laplacian 172 193 Laplacian radial 318 Lattice 35 Leach, P.G.L. 204 [163] Left invariant 48 50 72 Left Lie algebra 48 56 Left multiplication 36 Legendre transformation 126 127 323 Legendre — Hadamard condition 346 Legendre, A.M. 126 323 346 Leibniz rule 20 224 Leibniz, G.W. 20 224 Lemma Cartan's 26 Lemma Poincare 29 286 Level set 16 44 174 440 Levi-Civita, T. 389 Lewy, H. 178 448 [149] Lie algebra 49 54 58 71 78 254 268 444 Lie algebra left 48 56 Lie algebra of differential operators 86 212 Lie algebra of vector fields 56 120 424 Lie algebra right 48 56 Lie algebra, canonical form for 59 Lie algebra, cohomology 88 Lie algebra, representation 77 Lie bracket 21 23 28 49 51 69 78 120 257 417 Lie derivative 69 232 Lie derivative, higher order 102 Lie determinant 194 201 202 Lie group 32 48 53 54 254 268 435 441 Lie group local 53 444 Lie group, matrix 33 54 72 76 288 Lie series 21 Lie subalgebra 53 Lie subgroup 33 53 Lie — Baecklund vector field 119 Lie, M.S. xiii 3—5 21 53 59 61 119 126 127 131 134 136 146 152 187 200 203 204 205 221 238 242 318 327 356 401 407 408 444 [150—157] Lifted coframe 305 353 366 460 Line bundle 10 Line projective 20 36 81 Line segment 64 Linear 426 Linear differential equation 60 211 218 Linear elasticity 346 Linear fractional function 156 195 205 Linear fractional transformation 36 46 81 114 148 181 Linear polynomial 79 Linear quasi- 255 411 429 Linear system 209 Linear transformation 33 Linearization 186 209 400 406 Linearly dependent 25 Linearly independent 218 Littlejohn, L.L. 217 [158] local 3 10 35 Local coordinate 32 252 Local diffeomorphism 12 Local equivalence 257 Local invariant 45 Local Lie group 53 444 Local transformation group 35 Locally 10 35 Locally effective 38 56 86 143 200 Locally free 38 42 58 94 Locally invariant 64 Locally regular 436 Locally solvable 177 209 413 Locally transitive 67 Lowering operator 80 Macaulay's theorem 167 169 Macaulay, F.S. 167 169 [159] MacCallum, M.A.H. 394 [137] [141] Mackey, G.W. 75 82 [160] Magadeev, B.A. 251 [161] Magri, F. 366 [162] Mahomed, F.M. 204 [163] Majorant method 448 Mal’cev, A.I. 445 [164] Manifold 8 29 32 35 253 Manifold classifying 266 268 271 396 435 437 441 471 Manifold covering 441 Manifold pseudo-Riemannian 282 387 Manifold Riemannian 282 377 386 389 Manifold space-time 394 MAP 10 11 22 Map covering 12 54 271 441 Map exponential 53 Map regular 11 Map structure 263 270 277 367 Map, canonical form for 11 Map, equivalence problem for 11 Map, overlap 8 Map, singularity of 11 Maple 309 359 Marsden, J.E. 221 244 [165] Martinet, J. 31 [166] Maschke, H. 408 [167] Mathematica xv 309 359 Matrix 33 42 49 Matrix exponential 53 Matrix Hessian 173 345 Matrix Jacobian 11 22 26 139 176 423 438 Matrix multiplier 83 Matrix symmetric 43 44 282 387 Matrix total Jacobian 166 230 235 Matrix, canonical form for 42 282 387 Matrix, differential operator 91 Matrix, Euler — Lagrange 249 Matrix, Lie group 33 54 72 76 288 Matrix, multiplier representation 90 93 Matrix, rank of 455 467 469 Matrix, skew-symmetric 34 39 43 54 73 76 Maurer — Cartan coframe 254 268 275 441 Maurer — Cartan form 71 254 435 Maurer — Cartan form modified 374 376 394 462 Maximal integral submanifold 424 Maximal rank 11 16 176 445 Maximum 222 Mechanics 345 Mechanics classical 31 Mechanics fluid 18 198 Mechanics Hamiltonian 31 34 126 127 221 Mechanics quantum 31 75 78 211 212 Method of characteristics 430 Metric 377 385 Metric complete 445 Metric Euclidean 34 299 377 Metric Finsler 333 Metric Minkowski 393 Metric pseudo-Riemannian 282 387 Metric Riemannian 272 282 291 333 386 394 445 Metric tensor 387 Michel, L. 204 [142] Mikhailov, A.V. 186 [168] Miller, W.Jr. 82 209 [125] [126] [169] Mills, R.L. 198 Minimum 222 Minkowski metric 393 Minkowski, H. 393 Mizel, V.J. 222 [16] Modular form 102 Moebius band 10 Moebius transformation 36 Moebius, A.F. 10 36 Momentum 31 242 Momentum angular 242 Monomial 168 334 Morikawa, H. 217 [170—172] Moving frame 156 Multi-Hamiltonian system 272 367 Multi-index symmetric 112 223 Multi-index, strictly increasing 25 254 Multiple integral 345 Multiple root 98 Multiplication 32 36 Multiplication operator 86 Multiplier 82 91 109 425 Multiplier determinantal 86 95 Multiplier fundamental 89 Multiplier infinitesimal 85 87 92 236 247 Multiplier representation 82 93 106 425 Multiplier representation Jacobian 84 92 Multiplier representation, equivalent 87 Multiplier representation, fundamental 95 120 148 215 Multiplier representation, matrix 90 93 Multiplier representation, trivial multiplier 88 Multiplier trivial 83 Multiplier, divergence 154 Multiplier, equation 82 Multiplier, matrix 83 Multiplier, total Jacobian 165 Multiply valued 262 267 Murillo, R. 408 [173] n-integrable 413 Nagano, T. 425 [174] Narasimhan, R. 25 424 [175] Natural boundary 198 Neuman, F. 211 [176] Newell, A. 100 186 [177] Newton, I. 225 Newtonian variational problem 225 Noether's theorem 221 244 246 Noether, E. 221 242 244 246 [178] Noncharacteristic 448 Nonclosed two-form 31 367 Nonconstant curvature 384 Nonconstant type 294 306 350 471 Nondegenerate 338 346 Nondegenerate Lagrangian 225 227 323 Nonlocal 185 Nonsingular 369 Nontangential 187 Norm 34 37 382 normal 34 38 178 203 Normalizable 79 Normalization 291 295 299 305 309 359 395 Normalization infinitesimal 360 Normalizer subgroup 55 190 Null Lagrangian 225 234 Number theory 198
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