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