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| Lefschetz S. — Differential Equations: Geometric Theory |
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| Предметный указатель |
 -set of a path 228
Adjoint equation 66
Adjoint equation, systems 61
Analytic (analytical) arc 24
Analytic (analytical) curve 24
Analytic (analytical) functions of several variables 21
Analytic (analytical) manifold 21
Analytic (analytical) matrix 20
Analytic (analytical) p-cell, elementary 24
Analytic (analytical) vector function 21
Analyticity properties of solutions of diff. eqs. 43
ARC 6
Arc without contact 211
Arc, analytical 24
Autonomous system 46
Axis of path cylinder, ring, rectangle 52 53 183
Base for the solutions of a linear system or diff. eq. 58
Base for the solutions of a single eq. 58
Base for the solutions of a vector space 10
Basic system 88
Bendixson's theorem on limit sets 230
Bendixson's theorem on limit sets, criterium for limit-cycles 238
Block of a matrix 14
box 37
Box, center of 37
cell 5
Cell, p-cell 5
Center 187 192
Characteristic exponents 73
Characteristic polynomial, of a matrix 13
Characteristic roots, of a matrix 13
Circuit 360
Circuit, deformation of 361
Circuit, homotopy of 360
Class  , function of 25
Closed arc 6
Closed cell 5
Closed set 4
Compact set or space 6
Complete family of periodic solutions 174
Component of a set 8
Component of a vector 10
Condensation point 5
Connectedness 7
Continuity properties of solutions of diff. eqs. 36
Continuous function 5
Continuous matrix 20
Continuous transformation 5
Convergent series of matrices 15
Convexity condition 108
Covering of a space by open sets 6
Critical point 36
Critical point, elementary 182
Critical point, general 208
Curve, analytical 24
Definite function, positive or negative 113
Derivative of a matrix 11
Diameter of a set 2
Differentiability properties of solutions of diff. eqs. 40
Dimension of a vector space 10
Direct sum of vector spaces 10
Distance between two points 2
Distance from a point to a set 2
Divergence of a vector 157
Domain of analyticity of a diff. eq. 44
Domain of continuity of a diff. eq. 35
Elementary critical points 182 188
Elliptic sector 219
Equation of Cartwright — Littlewood 279
Equation of Hill 337
Equation of Levinson 279
Equation of Levinson — Smith 279
Equation of Lienard 267
Equation of Mathieu 337
Equation of Van der Pol 272
Euclidean space 3
Euler — Poincare characteristic of a two-dimensional manifold 28
Existence theorem 31
Exponential of a matrix 18
Extension of solution of a diff. eq. 35
Fan 219
Focus 220
Focus, stable, unstable 187 192
Function of a matrix 17
Function of fixed sign, positive or negative 113
Function, continuous 5
Function, definite, positive or negative 112
General solution of a diff. eq. 39
Genus of a two-dimensional manifold 28
Green's formula 67
Half path, positive, negative 228
Holomorphic function of several variables 21
Holomorphic vector function 21
Homeomorphic spaces 5
Homeomorphism 5
Homotopy 360
Homotopy, cylinder 360
Hyperbolic sector 219
Implicit function theorem 23
INDEX 195 360
Index of a closed path 199
Index of a curve 195
Index of a point 195
Index of an elementary critical point 196
Instability 78
Integral of a matrix 12
Integral of a system of diff. eqs. 54
Integral of a vector 11
Jordan curve 6
Jordan — Schoenflies theorem 9
Kronecker deltas 10
Liapunov function 113
Liapunov function, expansion theorem 96
Liapunov function, numbers 152
Liapunov function, strong 195 225 228
Limit-cycle 223
Limiting sets of paths, position of limit-cycles 342
Limiting sets of paths, positive, negative 225 228
Linear system 55
Linear system with constant coefficients 69
Linear system with periodic coefficients 73
Linear system, homogeneous 55
| Lipschitz condition 30
Local phase-portrait at critical point 218
Logarithm of a matrix 18
Majorante 22
Manifold of section 161
Manifold, differentiable 27
Manifold, Euler — Poincare characteristic of 28
Manifold, genus of 28
Manifold, non-orientable 27
Manifold, orientable 27
Manifold, two-dimensional 28
Manifold, vector field on 28
Matrix 9
Matrix, analytical 20
Matrix, derivative of 11
Matrix, exponential of 18
Matrix, function of 17
Matrix, function of scalars 19
Matrix, integral of 12
Matrix, inverse of a square 10
Matrix, limit of 15
Matrix, logarithm of 18
Matrix, nilpotent 12
Matrix, non-critical 119
Matrix, non-singular 10
Matrix, norm of 11
Matrix, normal 14
Matrix, series of 15
Matrix, series of, absolutely convergent 16
Matrix, series of, uniformly convergent 16
Matrix, similar 13
Matrix, stable 88
Matrix, trace of 12
Matrix, transpose of 12
Matrix, triangular 12
Metric 2
Metric, space 1
Metrization 1
Metrization, equivalent 2
Neighborhood of a point or set 4
Nilpotent matrix 12
Node, stable, unstable 184 189
Non-analytical systems 259
Non-homogeneous system 72
Non-singular matrix 10
Non-singular matrix, solution of a diff. eq. 62
Non-unit (as power series) 26
Norm of a matrix 11
Norm of a vector 11
Normal matrix 14
Normal system in the sense of Liapunov 154
Open set 4
Path 47
Path, closed 48
Path, cylinder 50
Path, polygon 230
Path, rectangle 52 182
Path, ring 53
Perturbation method 312
Phase-portrait 181
Phase-portrait, local 218
Picard's method of successive approximations 31
Poincare's closed path-theorem 232
Poincare's expansion theorem 44
Poincare's index theorem 366
Product space 2
Projective coordinates 7
Projective plane 7
Projective real 7
Projective space 7
Quasi-harmonic system 312
Quasi-harmonic system, stable 124
Quasi-harmonic system, unstable 124
Regular system in the sense of Liapunov 154
Regular transformation 23
Saddle point 186 190
Self-excited system 313
Separatrix 223
Series of matrices 15
Series of matrices, absolutely convergent 16
Series of matrices, uniformly convergent 16
Series of vectors 15
Small parameters, method of 313
Space 1
Space, metric 1
Sphere 5
Sphere, p-sphere 5
Spheroid 2
Spheroid, center of 2
Spheroid, radius of 2
Stability 76
Stability of mappings 84
Stability of trajectories 83
Stability, asymptotic 78 83
Stability, conditional 78 83
Stability, exponentially asymptotic 85
Stability, orbital 83
Stability, structural 250
Stability, uniform 78
Stability, uniform, in product spaces 122
Stroboscopic method according to Minorsky 325
Stroboscopic subharmonics 322
Systems linear 55
Systems linear, homogeneous 55
Systems linear, normal, regular in the sense of Liapunov 154
Systems linear, quasi-harmonic 170
Systems linear, quasi-linear 170
Systems linear, quasi-linear, of periodic solutions 170
TO curve 242
Topologically equivalent spaces 5
Trajectory 35
Transformation, of real vector space 14
Transformation, regular 23
Transformation, topological 5
Triangular matrix 12
Uniform stability 78
Unit (as power series) 26
Vector space 9
Vector space, base of 10
Vector space, dimension of 10
Vector space, direct sum of 10
Vector space, real 14
Well-behaved set 96
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