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



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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
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Предметный указатель
Invariant, form      395
Invariant, left- invariant, or right-invariant, vector field on a Lie group      412
Inverse image      349
Invertible jet      366
Involution functions in involution      42 101 111
Involution, forms in involution      10
Isobaric polynomials      371
Isochronous, family of deformation      399
Isochronous, folding fields      374
Isotropic, immersion      92
Isotropic, submanifold      92
Isotropic, vector subbundle      38
Isotropic, vector subspace      13
Isotropy subgroup      422
Jacobi, bracket      320
Jacobi, conformal Jacobi morphism      339
Jacobi, identity      348
Jacobi, morphism      338
Jacobi, structure      336
Jacobi, theorem      486
Je, k-th order je, of a map      365
Kahlerian structure      42
Kernel, of a bivector      9
Kernel, of a p-form      2
Kernel, of a Pfaffian system      383
Killing form      257
Kinematical state, space of kinematical      247
Korteweg — de Vries equation      180
Kostant, Guillemin and Sternberg's theorem      159
Kowalevska problem      266
Lagrange — Grassmann manifold      18 451
Lagrange, equation      77 79
Lagrangian, function      77
Lagrangian, immersion      92
Lagrangian, submanifold      92
Lagrangian, system      77
Lagrangian, vector subbundle      38
Lagrangian, vector subspace      11 13
Laplacian      51
Lax pair      268
Leaf, of a (generalised) foliation      385
Leaf, symplectic leaf of a Poisson manifold      130
Left-trivialisation      205
Legendre, involution      331 333
Legendre, morphism      73
Legendre, projective Legendre, transformation      314
Legendre, submanifold      311
Legendre, transform      75
Legendre, transformation      73
Lepage, T., decomposition theorem      46 49
Lepage, T., divisibility theorem      47 49
Lepage, T., theorem on exterior forms      5
Levi — Civita connection      374
Liapunov, function      104
Liapunov, theorem      104
Lie, algebra      411
Lie, algebra of a Lie group      413
Lie, derivative      350
Lie, group      409
Lie, subalgebra      411
Lie, subgroup      414
Lie, third theorem of Lie      414
Lie-Poisson structure      108
Lie-Poisson structure, modified      109
Lifting canonical lifting to the tangent bundle      346
Lifting of a diffeomorphism to the cotangent bundles      66
Lifting of an action to the cotangent bundle      192
Linear, part (of an affine action)      440
Linear, section of a projection      448
Liouville, automorphism      313
Liouville, fibered Liouville, manifold      307
Liouville, form      59 306 380
Liouville, isomorphism      313
Liouville, manifold      305
Liouville, natural Liouville form      306
Liouville, s-form      68
Liouville, structure      305
Liouville, Theorem      167
Liouville, vector field      64 302
Local, group      97 347 424
Local, Lie algebra      339
Local, trivialixation      366
Mass, center of mass, of a material body      248
Mass, total mass, of a material body      248
Material point      246
Mathieu transformation      67
Maximal, compact subgroup      439
Maximal, integral curve      346
Maximal, integral manifold of maximal dimension      384
Method of characteristics      475
Momentum, angular momentum      200 252
Momentum, linear momentum      200
Momentum, map      189 193 194
Morphism, conformal Jacobi morphism      339
Morphism, Jacobi morphism      338
Morphism, of almost linear bundles      370
Morphism, of cohomologies      434
Morphism, of complexes      434
Morphism, of principal bundles      280
Morphism, of surjective submersions      54 67
Morphism, Poisson morphism      114
Morse family      466
Motion of a Hamiltonian system      102 247
Multiple points      344
Mutually orthogonal      see “orthogonal”
Neutral component of a Lie group      414
Noether's theorem      197
Nonautonomous differential equation      355
Noncharacteristic Cauchy data      474 481
Nondegenerate, Poisson tensor      112
Nondegenerate, pseudohermitian form      27
Normal coordinates      418
One-parameter family of deformations      399
One-parameter group      347
One-parameter subgroup of a Lie group      416
Orbits, of a family of diffeomorphisms      388
Orbits, of a group action      422
Orientable vector bundle      68 290
Orientable, manifold      68 290
Orientable, transversally orientable, Pfaffian equation      290
Origin      369
Orthogonal, elements in a symplectic vector space      10
Orthogonal, group      30
Orthogonal, mutually completely orthogonal symplectic actions, operator      30
Orthogonal, mutually orthogonal, symplectic actions      228
Orthogonal, vector subbundles      38
Orthogonal, vector subspaces      10 183
Paxakahlerian structure      140
Pfaffian, equation      277
Pfaffian, structure      289
Pfaffian, system      382
Phase, extended phase, space      492
Phase, function      472
Phase, space      102 251 490 492
Physical space      246
Poincare — Cartan integral invariant      83 327
Poincare's lemma      361 363
Poinson's theorem      261 262
Poisson, action      193
Poisson, algebra      108
Poisson, bracket      42 100 107
Poisson, canonical Poisson, structure      108
Poisson, infinitesimal automorphism      121
Poisson, manifold      107
Poisson, modified canonical Poisson (or Lie-Poisson) structure      109
Poisson, morphism      114
Poisson, structure      42 107
Poisson, tensor      109
Poisson, vector space      8
Polar, decomposition      31
Polar, of a function group      119
Positive-definite, self-adjoint operator      30
Positive-definite, symmetric bilinear form      26
Presymplectic      105
Primitive form      44
Principal, bundle      279
Principal, direction (or axis, or momentum) of inertia      258
Principal, homogeneous space      420
Projectable, Pfaffian equation      299
Projection, of a Pfaffian equation      299
Projective bundle      283
Pseudo-adapted complex operator      29
Pseudohermitian form      27
Pull-back, of a form      342 349
Pull-back, of a Pfaffian equation      298
Pull-back, of a vector field      349
Quasiperiodic flow      167 177
Rank, constant rank map      343
Rank, of a bivector      9
Rank, of a generalised distribution      382
Rank, of a generalised Pfaffian system      382
Rank, of a p-form      2
Rank, of a Poisson structure      112
Rank, symplectic rank      12
Real, form      27
Real, symplectic manifold      106 141 218 222
Real, symplectic space      20
Real, vector subspace      27
Reduced, Hamiltonian, or Hamiltonian system      143 219
Reduction, symplectic reduction      141
Reeb vector field      291
Regular, action      423
Regular, function      73
Regular, value      345
Representation, linear representation, of a Lie algebra      424
Representation, linear representation, of a Lie group      421
Rotations, group of rotations      430
Schouten bracket      335
Second-order differential equation      72 371
Section (of a vector bundle)      342
Self-adjoint operator      30
Self-orthogonal symplectic action      229
Semi-basic differential form      56 68 357
Semidirect product      429 431
Semisimple Lie algebra      436
Separates (Hamiltonian system which separates)      227
Signature of a triplet of Lagrangian subspaces      455
Simple, action      423
Simple, foliation      394
Simple, form      44 49
Skewadjoint operator      30
Solution, generalized solution, of a first-order partial differential equation      474 478
Solution, of a differential system      366
Solution, of a second-order differential equation      372
Source, mapping      366
Source, of a map      365
Spanned, distribution spanned, by a family of vector fields      389
Spray      373
Stabilizer      422
Stable, in the sense of Liapunov      104
Stable, relatively stable, modulo G      242
Standard fiber      366
States (contact manifold of states)      331
Stationary motion      239
Stefan and Sussman theorem      389
Strict, symplectic reduction      141
Strictly contact structure, or manifold      285
Strong momentum map or generalised Hamiltonian      190 194
Submanifold      343
Submanifold, immersed submanifold      343
Submersion      343
Suspension of a Morse family      472
Symmetric, linear map      449
Symmetric, operator      30
Symmetries (Lie group of symmetries, of a Hamiltonian system      238
Symplectic, action      186 193
Symplectic, automorphism      7
Symplectic, cocycle      445
Symplectic, form      6 90
Symplectic, group      7
Symplectic, immersion      92
Symplectic, leaf of a Poisson manifold      130
Symplectic, Liouville structure (or manifold)      305
Symplectic, manifold      36 63 90
Symplectic, rank      12
Symplectic, reduction      141
Symplectic, structure on a manifold      36 63 90
Symplectic, structure on a vector bundle      36
Symplectic, structure on a vector space      6
Symplectic, submanifold      92
Symplectic, vector bundle      36
Symplectic, vector space      6
Symplectic, vector subbundle      38
Symplectic, vector subspace      13
Symplectically regular      142
Symplectification, of a contact manifold      309
Symplectification, of a contact vector field      318
Symplectomorphism (local or global)      94
Tangent, bundle      341
Tangent, map      342
Tangent, space      341
Tangent, to the k-th order      365
Target, mapping      366
Target, of a map      365
Time      246 492
Time-dependent, differential form      356
Time-dependent, function      86
Time-dependent, vector field      86 354
Torsion of a connection      381
Total space (of a bundle)      341
Trajectory of a vector field      346
Transition function      280
Transitive action      420
Transitive action, simply transitive action      420
Translation, group of translations      430
Translation, on a Lie group      410
Transversality      344
Transverse, canonical transverse, field      72
Transverse, field      72
Transverse, maps      344
Transverse, submanifolds      345
Transverse, weakly transverse      150
Trivial bundle      281
Trivialization, of a differentiable fibration      366
Trivialization, of a principal bundle      280 281
Tubular neighborhood      357
Unitary group      33
Van Est's theorem      439
Vanishes (form which vanishes on a submanifold      3
Velocities, of order k, or k-velocities      367
Velocities, vector field of velocities, of a rigid body      248
Vertical, 1-graph (of a function)      334
Vertical, 1-jet (of a function)      334
Vertical, bundle (of a Pfaffian structure)      292
Vertical, differential      71
Vertical, differential 1-form      54 57
Vertical, tangent bundle      54 469
Virtual motion      82
Volume form      68
Weinstein theorems      153 155 158
Zero of a vector field      104 347
Zero-section      369
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