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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 |
 -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  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  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  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
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