Главная    Ex Libris    Книги    Журналы    Статьи    Серии    Каталог    Wanted    Загрузка    ХудЛит    Справка    Поиск по индексам    Поиск    Форум   
blank
Авторизация

       
blank
Поиск по указателям

blank
blank
blank
Красота
blank
Libermann P., Marle Ch.M. — Symplectic Geometry and Analytical Mechanics
Libermann P., Marle Ch.M. — Symplectic Geometry and  Analytical Mechanics

Читать книгу
бесплатно

Скачать книгу с нашего сайта нельзя

Обсудите книгу на научном форуме



Нашли опечатку?
Выделите ее мышкой и нажмите Ctrl+Enter


Название: Symplectic Geometry and Analytical Mechanics

Авторы: Libermann P., Marle Ch.M.

Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Количество страниц: 541

Добавлена в каталог: 05.07.2008

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
blank
Предметный указатель
$L_{p}$-structure      291
1-graph of a function      312
Abelian ideal of a Lie algebra      436
Acceleration      373
action      86
Action symplectic      186 193
Action, angle coordinates      176
Action, elementary      86 328
Action, Hamiltonian      188 193 104
Action, linear of a Lie group      421
Action, of a Lie algebra      424
Action, of a Lie group      419
Action, of R on $T^{k}M$      370
Action, Poisson      193
Action, strongly Hamiltonian      190 193 194
Adapted, canonical basis adapted, to a pair of Lagrangian subspaces      16
Adapted, charts      343 393
Adapted, complex operator      29
Adjoint, of a form      12 43 48
Adjoint, of a linear operator      30
Adjoint, representation      425 426
Admissible Hamiltonian      144
Affine, action      439
Affine, group of affine, Euclidean displacements      430
Affine, representation      439 442
Almost complex structure      41
Almost Hermitian structure      42
Almost Kahlerian structure      42
Almost linear, bundle      370
Almost linear, mapping      370
Almost linear, space      370
Almost symplectic structure, or form      36 63
Angle-action coordinates      176
Angular, coordinates      166
Angular, momentum of a rigid body      252
Angular, velocity of a rigid body      247
Annihilated (elements annihilated, by a Lie-algebra action)      436
Annihilator, of a generalized distribution      383
Annihilator, of a vector subbundle      38
Annihilator, of a vector subspace      2
Arnold and Aves's theorem      170
Associated, charts      342
Associated, cocycle with a momentum map      201 203
Associated, cocycle with an affine action      440 442
Associated, cohomology classes with a Hamiltonian action      203
Associated, mappings at order k, or k-associated      378
Associated, momentum map with a generalised Hamiltonian      189
Associated, Poisson structure with a cocycle      210
Associated, Poissson structure with a symplectic structure      108
Associated, principal bundle with a rank 1 vector bundle      282
Associated, reduced Hamiltonian with s point of      219
Associated, reduced symplectic manifold with a point of $\mathcal{G}$      218
Associated,, Lie-algebra homomorphism with a Lie-group homomorphism      427
Atlas of a principal bundle      282
Automorphism, infinitesimal of a Pfaffian equation      280
Automorphism, of a Pfaffian equation      278
Autonomous differential equation      355
Base, of a submersion      54
Base, of a vector bundle      341
Basic differential form      57 68
Bracket, in a Lie algebra      411
Bracket, of two vector fields      348
Bundle, cotangent      341
Bundle, of exterior differential forms      341
Bundle, of tensors      341
Bundle, principal      279
Bundle, projective      283
Bundle, tangent      341
Bundle, vector      341
C-closed form      122
Canonical, basis      6
Canonical, chart      104 135 325
Canonical, coordinates,      51 135
Canonical, projection of a vector bundle      341
Canonical, projection of the tangent or cotangent bundles      341
Canonical, symplectic form      8
Canonical, symplectic structure on a cotangent bundle      63
Canonical, transformation      495
Canonical, transverse field      72
Canonically conjugate      140
Caratheodory — Jacobi — Lie theorem      51 136
Cartan, E., theorem on exterior 2-forms      4
Cartan, E., theorem on Lie subgroups      414
Cartan, E., theorem on symplectic manifolds      136
Cartan, H., formula      351
Cauchy data      346 355 474 479
Characteristic curves      479
Characteristic distribution      406 479
Characteristic field      112 323
Characteristic foliation of a differential form      407
Characteristic space      9 112
Characteristic subspace of A. differential form      406
Characteristic vector field of a differential form      405
Christoffel symbols      367 373
Class, of a differential form      406
Class, of a Pfaffian equation      284
Class, of a Pfaffian form      285
Coadjoint representation      428
Coboundary      433
Coboundary operator      434
Cochain      433
Cochain homogeneous, of a Lie group      43
Cochain, non-homogeneous, of a Lie group      437
Cochain, of a Lie algebra      435
Cocycle      433
Codifferential      48
Cogeodesic      378
Cohomology, of a complex      433
Cohomology, of a Lie algebra      435
Cohomology, of a Lie group      437
Cohomology, relative, of a Lie algebra      436
Cohomology, space      433
Coisotropic, immersion      92
Coisotropic, submanifold      92 183
Coisotropic, vector subbundle      38 183
Coisotropic, vector subspace      13
Compact type      419
Compatible (pair of vector fields compatible with a map)      349
Complete, generalized complete, integral (local or global      488 489
Complete, integral (local or global)      485 486
Complete, vector field      347
Completely distribution      384
Completely Hamiltonian system      160
Completely integrable, differential system      366
Complex, of vector spaces      433
Complex, operator      27 40
Complex, vector bundle      40
Complex, vector subspace      27
Components of a k-velocity      368
Configuration      246
Configuration extended configuration space      492
Configuration space      247 490 492
Configuration space-time      329
Conformal, infinitesimal transformation      352
Conformal, Jacobi structure      338
Conformally symplectic (locally or globally)      50
Connected fibers (symplectic reduction with connected)      141
Connection      367
Connection symmetric      367 377
Connection, linear connection      367
Conormal bundle conormal to a submanifold      93
Conormal, bundle conormal to the fibers of a submersion      55
Constrained extrema      242
Contact, element      276 312
Contact, field      317
Contact, form      285
Contact, Hamiltonian      319
Contact, manifold      285
Contact, structure      285
Contact, transformation      285
Contact, vector bundle      334
Contact, vector field      317
Contragredient representation      428
Coset (left or right coset in a Lie group)      414 415
Cotangent, bundle      341
Cotangent, space      341
Covelocity      376
Critical, point of a differentiable map      238
Critical, point of a vector field      104 347
Critical, subset, or submanifold, of a Morse family      467
Curvature of a connection      367
Darboux's theorem, for Pfaffian equations or forms      286
Darboux's theorem, for symplectic structures      51 135
De Rham cohomology      435
Derivation (of an algebra)      351 411
Derivative, Lie derivative      350
Derivative, of a function, with respect to a vector field      348
Determines (form which determines a Pfaffian equation)      278
Diffeomorphic Morse families      472
Differentiable, fibration      366
Differentiable, generalized distribution      382
Differentiable, generalized Pfaffian system      382
Differentiable, section      382
Differentiable, space of differentiable forms      342
Differentiable, space of differentiable functions      342
Differentiable, space of differentiable vector fields      342
Differential, equation      346
Differential, of order k, or k-differential      376
Differential, system of order k      366 377
Direct image      349
Direct-product structure      429
distribution      276 393
Distribution, generalized      276 382
Distribution, of rank k, or k-distribution      393
Domain of a flow      347 355
Dual pair      119 211
Effective, action      420
Effective, form      44 49
Ellipsoid of inertia      261
Embedding      343
Energy      79 490
Energy, conservation of energy      80
Energy, equation of energy      329
Energy, kinetic energy      79 250
Energy, manifold of trajectories of given energy      146
Energy, potential energy      79
Equal (forms equal on a submanifold)      361
Equilibrium, point      104 239 347
Equilibrium, reduced to equilibrium      495
Equivalent affine actions or affine representations      441 443
Euler — Lagrange problem      265
Euler — Poinsot problem      260
Euler's equations, for the motion of a rigid body      254 255
Euler's equations, of a variational problem      81
Everywhere defined family of vector fields      387
Exact sequence of homotopies      460
Exchangeable forms      30
Exponential map, or mapping, of a Lie group      416
Exponential map, or mapping, of a spray      375
Extension, k-jet extension      366
Extension, of a function      294
Extension, of a map      342
Exterior product      342
Extremals      81
Fiber of a submersion      54
Fibered, dynamical system      293
Fibered, Liouville manifold      307
Fibered, product      54 345
First integral, of a distribution      402
First integral, of a Hamiltonian system      102
First integral, of a vector field      348
First order partial differential equation      473 478
Flow, of a time-dependent vector field      355
Flow, of a vector field      347
Flow, reduced flow      356
Foliation      393
Foliation generalised      385
Force of gravity      251
Free, action      420
Free, mechanical system      199
Frobenius' Theorem      393
Function group      107 119
Fundamental, 1-form and 2-form on a tangent bundle      97
Fundamental, group of the Lagrange — Grassmann manbifold      458
Fundamental, group of the symplectic group      458
Fundamental, symplectic form on a cotangent bundle      90
Fundamental, vector field      421
Generated, diffeomorphism generated, by a family of vector fields      387
Generated, invariant distribution generated, by a family of vectorfields      389
Generated, Lagrangian immersion generated, by a Morse family      467
Generated, symplectomorphism generated, by a generating function      487
Generated, system of generated      165
Generating function      93 487 495
Generators,of a discrete subgroup of $R^{n}$      16
Geodesic      373
Grassmann manifold      452
Guillemin and Sternberg's theorems      158 159
Hamilton — Jacobi equation      490 493
Hamilton, equation      79 102
Hamilton, principle of least action      86
Hamiltonian      98 102 109 490
Hamiltonian action      188 193 194
Hamiltonian contact Hamiltonian      319
Hamiltonian description      77
Hamiltonian extended Hamiltonian      492
Hamiltonian function      77
Hamiltonian generalized Hamiltonian      189 193 194
Hamiltonian strongly Hamiltonian action      190 193
Hamiltonian system      77 79 102
Hamiltonian vector field      98 106 109
Hamiltonian, locally Hamiltonian vector field      97 106 122
Hamiltonian, of constraints      146
Harmonic form      51
Hermitian form      28
hessian      377
Hodge's decopmposition theorem      51
Homogeneous, exterior differential form      302
Homogeneous, Hopf fibration      148
Homogeneous, of morphisms of complexes      434
Homogeneous, operator      359
Homogeneous, Pfaffian equation      302
Homogeneous, space of a Lie group      415
Homogeneous, vector field      302
Homomorphism of Lie algebras      411
Homotopy, lemma      359
Horisontal, bundle (of a contact structure)      292
Horisontal, distribution of a connection      367
Hyperregular function      73
Ideal of a Lie algebra      411
Ideal, derived ideal      411
Immersion      343
Inertia operator of a rigid body      250
Infinitesimal automorphism, of a differential form      352
Infinitesimal automorphism, of a Liouville structure      315
Infinitesimal automorphism, of a Pfaffian equation      279
Infinitesimal automorphism, of a Poisson structure      121
Infinitesimal automorphism, of a symplectic structure      97
Integral, curve      346 355
Integral, first integral      see “first”
Integral, invariant      395 401
Integral, manifold of a distribution      383
Integral, manifold of a Pfaffian equation      279 384
Integral, of a distribution      383
Integral, of a Pfaffian equation      279 383
Integral, submanifold of a k-form      279
Interior, automorphism      425
Interior, derivation      412
Interior, left interior product      2
Interior, product      2 48 342
Interior, right interior product      8 9
1 2
blank
Реклама
blank
blank
HR
@Mail.ru
       © Электронная библиотека попечительского совета мехмата МГУ, 2004-2017
Электронная библиотека мехмата МГУ | Valid HTML 4.01! | Valid CSS! О проекте