Schouten J.A., van der Kulk W. — Pfaffs Problem and Its Generalizations :: Электронная библиотека попечительского совета мехмата МГУ

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Schouten J.A., van der Kulk W. — Pfaffs Problem and Its Generalizations

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Название: Pfaffs Problem and Its Generalizations

Авторы: Schouten J.A., van der Kulk W.

Аннотация:

In its simplest form, the Pfaff problem (formulated by Pfaff in 1819) consists of determining the maximal integrable manifold of a Pfaffian system, i.e. of a system of vector fields in R^n. This book gives a solution of this problem and discusses various generalizations, giving an essentially complete treatment of the theory as it was known in 1949.

Язык:

Рубрика: Математика/Анализ/Дифференциальные уравнения/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1949

Количество страниц: 542

Добавлена в каталог: 15.04.2005

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Предметный указатель

$2\rho$ of $w_\lambda$       149
$2\rho$ of $w_{\lambda_1...\lambda_q}$       175f
$2\rho$ of $\mathfrak{N}_m$       279
$2\rho$ under C-transformations      280
$2\var{\rho}$ of $\mathfrak{N}_m$       285
$A^k_\lambda$       6 49
      20
$B^k_\beta$       18 20 21
$B^k_\lambda$       11
$B^\zeta_\beta$       21
$C^k_\lambda$       11
$C^x_\lambda$       21
$C^\zeta_\beta$       23
$C^\zeta_\lambda$       22
      175
-transformation      210 ff
-transformation, characteristic functions of infinitesimal      243 f 272
-transformation, field preserving      212
-transformation, generating function of      221
-transformation, rank of      216
-transformation, Rule I      215
-transformation, Rule II      219
-transformation      229 ff
-transformation, and $\mathfrak{N}_m$       347
-transformation, characteristic functions of infinitesimal      244 f 271
-transformation, field preserving      230
-transformation, generating function of      232
-transformation, Rule I      231
-transformation, Rule II      232
-transformation      224 ff
-transformation, and $\mathfrak{N}_m$       332
-transformation, characteristic function of infinitesimal      245 271
-transformation, field preserving      224
-transformation, generating function of      227
-transformation, Rule I      225
-transformation, Rule II      228
      185
$D^{..x}_{cb}$       88
      72
$e^k_\lambda$ , $e^k_\lambda$ in       5 6
$e^k_\lambda$ , $e^k_\lambda$ in , in       49
      1 2
, centred      1
, local      4 7
      2
      350 357
$K^{xy}$ , of $\mathfrak{N}_m$       278 283
$K^{xy}$ , of $\mathfrak{N}_m$ , under C-transformations      279
      207
      351 357
      185
(characters of Goursat system)      377 383
$T^{..x}_{jb}$       419
of $\mathfrak{N}_m$       281
$U_{cb}$ of $\mathfrak{N}_m$       283
, $V^{AB}$ of $\mathfrak{N}_m$       282
, $W_{BA}$ of $\mathfrak{N}_m$       281 f
$w_\lambda$ -rank of $\mathfrak{N}_m$       274
      61 ff
, connecting quantities      62
, reduction with respect to      63
, section with      63
in       33 ff
in , connecting quantities      39 40
in , mill form      39
in , parametric form      40
in , reduction with respect to      52
in , section With      52
      29 ff
-forming systems of vector fields      128 129
$\delta^k_\lambda$ (Kronecker symbol)      5
$\epsilon_1$ , $\epsilon_2$       55
$\mathfrak{E}^{k_1...k_n}$ , $\mathfrak{e}_{\lambda_1...\lambda_n}$       19
$\mathfrak{N}$       29
$\mathfrak{N}(\xi^k)$       29
$\mathfrak{N}_m$       207 273
$\mathfrak{N}_m$       283
$\mathfrak{N}_m$ $K^{xy}$       278
$\mathfrak{N}_m$       281
$\mathfrak{N}_m$ $U_{cb}$       283
$\mathfrak{N}_m$ , $V^{AB}$       282
$\mathfrak{N}_m$ $w_\lambda$ -rank      274
$\mathfrak{N}_m$ $\var{K}$ , $\var{k}$       285
$\mathfrak{N}_m$ and -transformations      347 275 332
$\mathfrak{N}_m$ canonical form of equations      332
$\mathfrak{N}_m$ class K      279
$\mathfrak{N}_m$ dis-homogenization      273 286
$\mathfrak{N}_m$ field dimension      208 274
$\mathfrak{N}_m$ field region      208 274
$\mathfrak{N}_m$ homogenization      273 286
$\mathfrak{N}_m$ index l      279
$\mathfrak{N}_m$ integrability      286 ff
$\mathfrak{N}_m$ integral- $\mathfrak{N}^'_{m}$ of class < K      320 ff
$\mathfrak{N}_m$ integral- $\mathfrak{N}_{m'}$       286 296
$\mathfrak{N}_m$ null form      273
$\mathfrak{N}_m$ parametric form      273
$\mathfrak{N}_m$ Poisson bivector      278
$\mathfrak{N}_m$ reduced form of equations      298
$\mathfrak{N}_m$ rotation class 2p      279
$\mathfrak{N}_m$ similarity class k      279
$\mathfrak{N}_{m-1}$ , $M_{m-1}$       208
$\mathfrak{S}_d^m$ -field      275
$\mathfrak{S}_d^m$ -field, $\tau_p$       433 436 452 456
$\mathfrak{S}_d^m$ -field, adjoint $'E_{m+d}$ -field of      420
$\mathfrak{S}_d^m$ -field, and Goursat systems      446 ff
$\mathfrak{S}_d^m$ -field, cases A, B, and C      425ff
$\mathfrak{S}_d^m$ -field, field dimension      418
$\mathfrak{S}_d^m$ -field, general integral-      455
$\mathfrak{S}_d^m$ -field, induced $\mathfrak{S}_{dp}^p$ -field      431
$\mathfrak{S}_d^m$ -field, integral-      418
$\mathfrak{S}_d^m$ -field, null form      457 ff
$\mathfrak{S}_d^m$ -field, parametric form      419
$\mathfrak{S}_d^m$ -field, preferred      423
$\mathfrak{S}_d^m$ -field, quasi-linear      418 445
$\mathfrak{S}_d^m$ -field, stationary $\mathfrak{S}_{dp}^p(\xi^k)$       436 f
$\mathfrak{S}_d^m$ -field, theorem of integrability of      296 423 437
$\mathfrak{S}_d^m$ -field, theorem of uniqueness      I 453 II 454 III 464
$\mathfrak{V}_{m-n}$ -fieid integrability of      296
$\mu_1,...,\mu_\omega$       103
$\nu$       199
$\sigma$ (species of Ooursat system)      388
$\tau$ of $\mathfrak{S}_d^m$ -field      433 436 452 456
$\var{K}$ , $\var{k}$ of $\mathfrak{N}_m$       285
$\zeta$ (s-number of Goursat system)      385
Abbreviated system      115 122
Absolute integral invariant of $v^{K}$       74
Absolute integral invariant of $[v^{K}]$       76
Absolute invariant field with respect to       44 96 98
Absolute invariant field with respect to       74 97 98 144 145
Absolute invariant field with respect to $[v^{K_{1}...K_p]$       132 184
Addition      8
Adjoint system      84
Adjoint' $E_{m+d}$ -field      420
Admitted infinitesimal point transformation      136 ff
Affine, geometry      32
Affine, group      1
Affine, space      1
Affinor, density      19
Affinor, inverse of      8
Affinor, matrix of      7
Affinor, pseudo-      3
Affinor, unity      7
Alexander, J.W.      10
Allowable coordinates      1
Alternated multiplication      13
Alternation      9
Analytic field      47
Analytic function      30
Analyticity in a region      33
Analytisches Plachenstuck      516

Anholonomic system      51
Arithmetic, manifold      29
Arithmetic, point      29
Auto isomorphic field      148 164
Auxiliary system      120
Basis      3 7
Basis, theorem      I 37 II 38
Basis, transformation      38 275
Behnke, H.      516
Bibliography      534
Bivector      13
Bivector, decomposition into blades      15
blades      15
Bracket expression, of Lagrange      246 ff
Bracket expression, of Poisson      246 ff 253
Burstin, C.      349 355
c,       149 175
C-transformation      199 ff
C-transformation, double homogeneous      232
C-transformation, field preserving      212
C-transformation, infinitesimal      241 ff
Canonical form      147
Canonical form, of $w_\lambd$       160 ff
Canonical form, of $w_\lambd$ with given initial conditions      170 ff
Canonical form, of $\mathfrak{N}_m$       332
Canonical form, of function group      260 269
Canonical form, of homogeneous equation      96
Canonical form, of homogeneous system      113
Canonical representation      147
Cartan, E.      v vi 73 136 148 151 153 160 172 173 199 349 350 355 358 377 378 385 387 388 410 416 417 461 475 502 529
Cartan, theorem of Cartan — Kaehler      358 ff
Cartan, theorem of integrability of      362
Cartan, theorem system      356
Cases A, B, C Grynaeus and the $\mathfrak{S}_d^m$ -field      425 ff
Cases A, B, C, D Grynaeus      187 ff
Cases I and II, of      150 ff
Cases I and II, of $w_\lambda$       176
Cases I, II, and III of $\mathfrak{S}_d^m$ -field      425 ff 428
Cauchy, generalized integration method of      313
Cauehy, A.      90
cell      32
Centred,       1
Chain, ordinary      441 443
Chain, regular      351 358
Chain, test for regular chains      397 ff
Characteristic function, of infinitesimal -transformation      243 f 272
Characteristic function, of infinitesimal -transformation      244 f 271
Characteristic function, of infinitesimal -transformation      245 271
Characteristic number of representation      147
Characteristics, of       89
Characteristics, of $w_\lambda$       152 161
Characteristics, of Goursat system      378
Characters      377
Class, of $w_\lambda$       149
Class, of $w_{\lambda_1...\lambda_q$       175
Class, of $\mathfrak{N}_m$       278
Class, of covariant q-vector fields      321 ff
Class, of function group      263
Class, of sets of geometric objects      146 ff
Clebsch, A.      vi
Closed Goursat system      355
Closed Goursat system, ring of      412
Comitant, differential      63 ff
Complete homogeneous systems      86
Complete homogeneous systems, existence theorem for      108
Complete integrability of $\mathfrak{S}_d^m$ -field      423
Complete non-homogeneous systems      110
Complete non-homogeneous systems, existence theorem for      111
Complete Riquier arrangement      507
Complete solutions      307
components      4
Components intermediate      8
Components of arithmetic point      29
Compounds-vector      14
Cone $\mathfrak{C}(E_p)$       435
Cone $\mathfrak{C}(\xi^k)$       429
Conjugate set of functions      157 ff
Conjugate systems      173
Connecting quantity, of in       20 21
Connecting quantity, of       62
Connecting quantity, of in       39 40
Contact-point      47
Contain      2
Contraction      8
Coordinate system      30 31
Coordinate-'s      2
Coordinates, allowable      1
Coordinates, transformation of      31
Courant, R.      50
Cutting off of BSC-system      473
D      64
Darboux, G.      vi
De Donder, Th.      73 129
Dead indices      5
Decomposition, of p-vector      15
Decomposition, of regular systems      53
densities      19 ff
Dependent functions      33
Derivative, Lie      72
Derivative, natural      48 64
Derivative, paramotrical      507
Derivative, principal      507
Derived system      86 103
Determinant, functional      30
Determinant, main sub-      38
Differential comitant      63 ff
Dimension of      6 6
Dimension of, support of      4
Dimension, field      47
Dimension, of domain      5 6
Dimension, of null form      35
Dimension, of parametric form      40
Diminished class, point of      149 186
Direction      2 48
Dis-homogenization of $\mathfrak{N}_m$       273 286
Div, divergence      64
Divisor of p-vector      14
Domain      4 6 10 11
Dragging along      70 ff
Eisonhart, L.P.      199 210 224 229 241 253 255 262 271
Elimination, theorem of      42
Eloment manifold $\mathfrak{M}_{m-1}$ , $M_{m-1}$       208
Engol, F.      vi 73 82 88 91 92 94 98 102 104 107 109 113 125 126 128 136 199 210 224 229 233 241 246 251 253 255 262 271 273 306 316 318 319
Enveloped,       84 86
Enveloped, normal system      84 199
Enveloped, Rule I      205
Enveloped, Rule II      206
Enveloping,       82 86
Enveloping, normal system      82 85
Equiscalar hypersurface      48
Equivalent systems of equations      34
Existence theorem, of Cauchy — Kowalewski      90
Existence theorem, of complete homogeneous system      108
Existence theorem, of complete non-homogeneous system      111
Existence theorem, of implicit functions      41
Existence theorem, of one homogeneous equation      91
Existence theorem, of one non-homogeneous equation      95
Existence theorem, of Riquier      508
Extended point transformation      217
Extension of incomplete system      102 ff
Extraordinary integral- of NRSG-system      503
Extraordinary points of NRSG-system      503
Faber, K.      vi 73 82 88 91 92 94 98 102 104 107 109 113 115 126 128 136 199 210 224 229 233 241 246 251 253 256 262 271 273 306 316 318 319
Field      47
Field dimension      47
Field dimension, of $\mathfrak{N}_m$       208 274
Field dimension, of $\mathfrak{S}_d^m$ -field      418
Field region      47
Field region, of $\mathfrak{N}_m$       208 274
Field, $\mathfrak{B}_{m-n}$       296

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