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

Field, $\mathfrak{S}_d^m$       275
Field, analytic      47
Field, autoisomorphic      148 164
Field, isomorphic      148 162
Field, of m-directions      61
Field, preserving C-transformations      212 224 230
Fixed indices      1
Forsyth, A.R.      vi
Free indices      9
Frobenius, G.      iv
Function group, homogeneous      262 ff 315
Function group, homogeneous canonical form      269
Function group, homogeneous class      263
Function group, non-homogeneous      256 ff 313
Function group, non-homogeneous, canonical form      260
Function group, non-homogeneous, null group      256
Function group, non-homogeneous, Poisson bivector      256
Function group, non-homogeneous, polar group      256
Function group, non-homogeneous, rank      256
Function group, non-homogeneous, singular functions      256
Functional, determinant      30
Functional, matrix      33
Functionals      50
Functions, supernumerary      166
Fundamental, determinant      30
Fundamental, matrix      33
Fundamental, region      33
g (genus)      351 358
g' (reduced genus)      378 384
Gauss, C.F.      vi
General intogral-, of $\mathfrak{S}_d^m$ -field      456
General intogral-, of Goursat system      377
General representation      147
Generating function      221 227 232
Geometric, manifold      29 32
Geometric, object      50
Geometric, point      32
Goursat system      355
Goursat system, $X_\nu$ -forming      355
Goursat system, characteristics      378
Goursat system, characters      377
Goursat system, closed      355
Goursat system, connected $\mathfrak{S}_d^m$ -field      445 ff
Goursat system, general integral-      377
Goursat system, genus      351 358
Goursat system, integral element      354
Goursat system, integral-      354
Goursat system, integral-      355
Goursat system, invariant $\sigma$       388
Goursat system, Kt      417
Goursat system, n'      417
Goursat system, reduced genus      378 384
Goursat system, ring of closed      412
Goursat system, s-number $\zeta$       385
Goursat system, scalar free      355
Goursat system, similarity class      378 417
Goursat system, theorem of integrability      358 ff
Goursat system, theorem of uniqueness I      359
Goursat system, theorem of uniqueness II      371
Goursat system, theorem of uniqueness III      372
Goursat, E.      vi 67 73 82 88 91 92 94 96 102 103 107 109 115 145 148 151 152 153 160 172 173 175 177 179 180 184 195 199 200 210 224 229 246 251 253 255 262 273 306 315 319 349 352 416
Grad, gradient, gradient field      48
Gradient product      65 135
Gradient transformation      168 ff
Grassmann, H.      vi
Grynaeus, cases A, B, C and $\mathfrak{S}_d^m$ -field      425 ff
Grynaeus, cases A, B, C, D      187 ff
Grynaeus, E.      185
Hilbert, D.      50
Holonomic       350
Homogeneous, canonical form of equation      96
Homogeneous, canonical form of system      113
Homogeneous, complete system      86
Homogeneous, existence theorem for complete system      108
Homogeneous, function group      262 ff 315
Homogenization of 91^      273 286
Hyperplane      2
Hypersurface      59
Identification of quantities of and       23
Identity of Jacobi, for irifinitesimal transformations      137
Identity of Jacobi, for Poisson brackets      247
Imbedding      33 40
Implicit functions, existence theorem of      41
Improper $E_{p-1}$       2
Independence, theorem of      34
Independent functions      33
Index, of $\mathfrak{N}_m$       278
Index, of set of functions with respect to $w_\lambda$       154 ff
Indices, dead      5
Indices, fixed      1
Indices, free      9
Indices, living      5
Indices, running      1
Indices, saturated      9
Induced $\mathfrak{S}_{d_p}^p$ -field      431
Infinitesimal, admitted point transformations      136 ff
Infinitesimal, C-transformation      241 ff
Infinitesimal, neighbourhood      48
Infinitesimal, point transformation      71 233
Infinitesimal, streamlines of transformation      233 ff
Inner orientation      4
Inner problem      84 85 349
Integrability, of $\mathfrak{B}_{m-n}$ -field      296
Integrability, of $\mathfrak{N}_m$       286 ff
Integrability, of $\mathfrak{S}_d^m$ -field      423 437
Integrability, of $\mathfrak{S}_d^m$ -fields      437
Integrability, of $\mathfrak{S}_d^{n-1}$ -field      296
Integrability, of Cartan-Kfthler      358 ff
Integrability, theorem of, of Cartan      352
Integrability, total      89 109
integral      84
Integral curves      89
Integral element      350 354
Integral element, regular      351
Integral invariant      see Absolute and relative
Integral over $\tau_q$       68
Integral, function      84
Integral, principal, function      91 108
Integral-'s in involution      350
Integral-, of $E_\tau$ -field      350
Integral-, of $w_\lambda$       338
Integral-, of Goursat system      354
Integral-, extraordinary      503
Integral-, general, of $\mathfrak{S}_d^m$ -field      155
Integral-, general, of Goursat system      377
Integral-, of $E_\tau$ -field      84 349
Integral-, of $\mathfrak{S}_d^m$ -field      418
Integral-, of Goursat system      355
Integral-, of NRSC-eystem      503
Integral-, regular      351 358
Integrating factor      98 99 100
Intermediate components      8
Invariant      see Absolute and relative
Inversion, theorem of      30
Invoiso of affinor      8
Involution, directions in      350
Involution, functions in      246 252
Involution, functions in, solution of differential equations in      306 ff
Irreducible, p-vector      14
Irreducible, tensor      12
Irregular systems of equations      35
Isomer      8
Isomorphic fields      148 162
jacobi      see Identity of
Jacobi, C.G.J.      vi
Jacobian system      104
Jacobian system, principal integral functions of adjoint system of      108
Jacobian system, principal solutions of      108
Jacobian system, special      105 115 122
Janet, M.      378 506

Joined neighbouring elements      209
Junction of and
K of $w_\lambda$       149 161
K of $w_{\lambda_1...\lambda_q$       175 f 179
K of $\mathfrak{N}_m$       279
K of Goursat system      417
k of Goursat system (n')      378 417
K under C-transformations      280
Kaehler, E.      1 18 33 35 37 53 82 349 355 358 402 410 417 461
Kernel letter      1
Klein, F.      81
Koenig, J.      510
Kowalewski, S.v.      90
Kronecker symbol $\delta^k_\lambda$       5
l of $\mathfrak{N}_m$       278
Lagrange bracket      246 ff
Lie in      2
Lie, derivative      72
Lie, differential      72
Lie, integration method of      313 ff
Lie, multiplier      129
Lie, S.      vi 82 118 131 136 138 139 143 199 208 209 210 224 229 241 251 253 255 256 262 272 273 306 307 315 319
Living indices      5
Local       47
m-dimensional surface      39
m-diroctions, field of      61
Manifold, arithmetic      29
Manifold, element      208
Manifold, geometric      29 32
Manifold, vector      208
Matrix, functional      33
Matrix, of aflfinor      7
Mayer system, abbreviation of      115
Mayer system, abbreviation of auxiliary system of      122
Mayer system, auxiliary system of      120
Mayer system, principal solution of      114
Mayer system, solution of      115 122
Mayer, A.      115 126
Mayor's theorem of integration      126
Measuring vectors      5 6 49
Minimal regular, parametric form      40
Minimal regular, systems of equations      35
Mixing      9
Multiplication      8
Multiplication, alternated      13
Multiplication, symmetric      12
n' (similarity class Goursat system)      378 417
Natani, L.      vi
Natural derivative      48 64
NBSC-system      474
NBSC-system, extraordinary points      503
NBSC-system, integral-      503
NBSC-system, parametrical vector coefficients      475
NBSC-system, principal vector coefficients      475
Neighbourhood      29
Neighbourhood, infinitesimal      48
Non-homogeneous, complete system      110
Non-homogeneous, equation      95
Non-homogeneous, existence theorem for complete systems      111
Non-homogeneous, function group      262 ff 313
Non-homogeneous, system      109
Normal form      147
Normal form, of q-vector fields      327
Normal form, of systems of Pfaff      327
Normal representation      147
Normal system of 's      45
Normal system of 's, enveloped      84 199
Normal system of 's, enveloping      82 85
Normal system of 's, reduction with respect to      45
NPRSC-system      477
NPRSC-system, prolongation of      493 ff
Null, $E_{4n-p}$       339
Null, dimension of, form      35
Null, form of in       39
Null, form of $\mathfrak{S}_d^m$ -fields      273
Null, form of Sf-fields      457 ff
Null, group      256
Null, manifold      34
Null, point      34 89
Null, regular, form      35
Null, space      2
Null, space of integral-      350
Null, supernumerary regular, form      35
Object, geometric      50
Operation       94
Operations, table of      611
Ordinary, chain      441 443
Ordinary, point of field      149 185
Ordinary, triplet      433 436
Orientation, inner      4
Orientation, outer      4
Orthonomic system      607
Orthonomic system, passive      506 508
Outer orientation      4
Outer problem      82
p-direction in       2 48
p-vector      13
p-vector density      19
p-vector, compound      14
p-vector, decomposition into blades      16
p-vector, divisor of      14
p-vector, geometric interpretation      17 ff
p-vector, irreducible      14
p-vector, pseudo      13
p-vector, simple      14
parallel      2 3
Parametric form, dimension of      40
Parametric form, minimal regular      40
Parametric form, of in       40
Parametric form, of $\mathfrak{N}_M$       273
Parametric form, of $\mathfrak{S}_d^m$ -field      419
Parametric form, regular      46
Parametric form, supernumerary regular      46
Parametrical, derivatives      607
Parametrical, variables      398 405 407
Parametrical, vector coefficients      475
Partial prolongation      469
Partial prolongation of PC-system      505
Passive orthonomic system      606 508
PC-system      605
Pfaff's problem, simple      vi vii
Pfaff, J.F.      vi
Pfaffian aggregate      28 514
Pfaffian equations, normal form of      327
PNRSC-system      477
Point, arithmetic      29
Point, extended, transformation      217
Point, extraordinary      503
Point, geometric      32
Point, infinitesimal, transformation      71 136 233
Point, of diminished class      149 185
Point, ordinary      149 185
Point, transformation      1
Poisson bivector, of $\mathfrak{N}_M$       278
Poisson bivector, of function group      266
Poisson brackets      246 ff 253
Poisson brackets, generalized      172 ff 272
Poisson brackets, Jacobian identity for      247 271
Polar, group      236
Polar, space      350
Preferred, $\mathfrak{S}_d^m$ -field      423
Preferred, RSC-ayatem      472
Principal, derivatives      507
Principal, integral functions      91 108
Principal, solutions      91 108 114
Principal, variables      398 405 407
Principal, vector-coefficients      475
Projection      3
Prolongation      463
Prolongation of      493 ff

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