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| Zelikin M.I. — Control Theory and Optimization, Vol. 1 |
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| Предметный указатель |
 -compatible functions 85
-compatible vector fields 85
Absolute 11 175
Adjoint representation of Lie algebras 92
Adjoint representation of Lie groups 92
Base of a fiber bundle 217
Basis forms of a distribution 220
Bellman equation 67
Bundle, canonical 218
Bundle, fiber of 217
Bundle, normal 50 218
Bundle, principal 199
Bundle, section of 219
Bundle, tangent 218
Bundle, vector (linear) 217
Canonical system of equations 16
Center of a Lie algebra 96
Chain rule 191
Clifford algebra 135
Clifford translation 152
Closed function 14
Commutator 86
Complexified matrix Riccati equation 187
Condition, Hilbert 15
Condition, Jacobi 30
Condition, Jacobi, strengthened 30
Condition, Legendre 26
Condition, Legendre — Caratheodory 252
Condition, Legendre — Weyl 242
Condition, strengthened Legendre 27
Condition, transversality 19
Condition, Weierstrass — Erdman 22
Conjugate point 28
Conjugating matrix 245
Connection, flat 235
Connection, general, on a bundle 227
Connection, linear 228
Connection, Riemannian (Levi — Civita) 231
Connection, symmetrical 230
Coordinates, conformal 209
Coordinates, matrix affine 264
Coordinates, matrix homogeneous 264
Coordinates, Plucker 115
Covariant derivative 230
Covering path 228
Cristoffel symbols 12 233
Curvature of connection 234
Curve, horizontal 227
Curve, modular 176
Curve, with scalar double ratio 143
Dirichlet functional 236
Dirichlet integral 210
distribution 220
Distribution, completely integrable 224
Distribution, involutive 222
Distribution, smooth 220
Double ratio 3
Equation, Bellman 67
Equation, Euler 7 214
Equation, Euler — Jacobi 215
Equation, Hamilton — Jacobi 24
Equation, Riccati 2
Equation, Riccati, complexified matrix 187
Equation, Riccati, matrix 31 61
Equation, Riccati, partial differential 260
Equation, Schwartz 203
Equation, variation 216
Euler equation 7 214
Euler — Jacobi equation 215
Exponential mapping 101
Exterior covariant differential 235
Fiber of a bundle 217
Field, Jacobi 216
Field, of extremals 53
Field, of extremals, -compatible vector 85
Field, potential 270
Field, vector 85
Field, vector, covariantly constant 232
Field, vector, left-invariant 86
Flow on the homogeneity domain of type I 192
Flow on the homogeneity domain of type II 194
Flow on the homogeneity domain of type IV 196
Focal point 42 55
Foliation 222
Foliation, Reeb 223
Form, basis, of a distribution 220
Form, connection 229
Form, contact 244
Form, curvature 235
Form, differential 45
Form, Killing 93
Form, Poincare — Cartan 18
Form, quadratic, for determination of angles 134
Fourth harmonic 147
Function, -compatible 85
Function, closed 14
Function, Weierstrass 44
Generalized unit disk 172
Geodesic 9
Geodesic inclination of a field 53 241
Geodesic symmetry 102
Geodesic symmetry with respect to a manifold 147
Group, fundamental 198
Group, Lie 80
Group, linear (matrix) 80
Group, linear (matrix) simple 96
Group, linear (matrix), semisimple 96
Group, structure, of a fiber bundle 217
Haar measure 98
Half-plane, generalized Siegel upper 177
Half-plane, Klein — Poincare 174
Half-plane, Lobachevsky 10
Hamilton — Jacobi equation 24
Hilbert condition 15
Hilbert invariant integral 54
Homogeneity (Cartan — Siegel) domain 166
Homogeneity (Cartan — Siegel) domain of type I 167
| Homogeneity (Cartan — Siegel) domain of type II 169
Homogeneity (Cartan — Siegel) domain of type III 171
Homogeneity (Cartan — Siegel) domain of type IV 172
Homogeneous space 100
Homotopic paths 78
Ideal generated by forms 221
Ideal of Lie algebra 95
Index, Maslov 160
Index, Morse 158
Index, Morse — Maslov — Arnold, in the form of Leray — Kashivara 159
Index, of a functional 35
Invariant integral 54
Isometry 100
Isometry, local 100
Jacobi condition 30
Legendre condition 26
Legendre — Caratheodory condition 252
Legendre — Weyl condition 242
Lie algebra 84
Lie algebra, abelian 96
Lie algebra, center of 96
Lie algebra, compact 98
Lie algebra, orthogonal, with involution 106 122
Lie algebra, semisimple 96
Lie algebra, simple 96
Lift of a manifold 54
Linear connection coefficients 229
Manifold, Grassmann 69 112
Manifold, Grassmann, complex 72
Manifold, Kahler 184
Manifold, Lagrange — Grassmann 119 156
Manifold, Legendre 50
Manifold, lift of a 54
Manifold, locally symmetrical at a point 102
Manifold, pseudo-Riemannian 99
Manifold, Riemannian 9
Manifold, simply connected 78
Manifold, stratified 177
Manifold, symmetrical 102
Manifold, topological 69
Matrix double ratio 131
Matrix Riccati equation 31 61
Maximal set of isoclinic planes 141
Minimum, strong 43
Minimum, weak 6
Monodromy matrix 198
Multiplicity of a point 35
Pair, symmetrical Riemann 105
Pairs of points, equidistant 138
Pairs of points, equivalent 139
Parallel translation 228
Plane, horizontal 69 112
Plane, isoclinic 132
Plane, isotropic 149
Plane, Lagrangian 117 156
Plane, semiorthogonal 154
Plane, stabilizer of 114
Plane, vertical 69 112
Planes Clifford parallel 153 155
Plucker embedding 116
Problem, associated extremal 28 215
Problem, brachistrochrone 5
Problem, Lagrange 63
Problem, linear-quadratic 64
Problem, Plataeu 208
Projection, natural 100
Quadruple of planes, biharmonic 148
Quadruple of planes, harmonic 131
Quaternion 73
Riccati equation 2
Riccati partial differential equation 260
Schwartz equation 203
Schwartz operator (derivative) 200
Schwartz operator, matrix 205
Second variation of a functional 25 215
Section of a bundle 219
Sets of congruent planes 142
Signature of a quadratic form 159
Skew-inner product 118
Space, bundle 217
Space, elliptic 151 154
Space, globally symmetrical 102
Space, isotropic 117
Space, symmetrical 102
Space, symmetrical, Hermitian 167
Stabilizer of a plane 114
Stratum 178
Strengthened Jacobi condition 30
Strengthened Legendre condition 27
Subalgebra of a Lie algebra 94
Subgroup, invariant (normal) 95
Subgroup, isotropy 100
Subgroup, of a Lie group 94
Subgroup, one-parameter 104
Subgroup, stationary 100
Submanifold, geodesic at a point 107
Submanifold, integral 50 224
Submanifold, totally geodesic 107
Subspace, horizontal 227
Subspace, vertical 227
Symplectic structure 83
Torsion of connection 233
Transformation, Caratheodory 244
Transformation, Cayley 185
Transformation, contact 244
Transformation, generalized linear-fractional 70 113
Transformation, Legendre — Weyl 240
Transformation, monodromy 198
Transvection 102
Transversality conditions 19
Triple Lie system 108
Variation equation 216
Variation geodesic 217
Vector, tangent 85
Vectors, skew-orthogonal 118
Weierstrass function 44
Weierstrass — Erdman condition 22
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