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Lefschetz S. — Differential Equations: Geometric Theory
Lefschetz S. — Differential Equations: Geometric Theory

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Название: Differential Equations: Geometric Theory

Автор: Lefschetz S.

Аннотация:

The surprisingly warm reception which greeted the author's monograph Lectures on Differential Equations (Princeton University Press 1946) provided the incentive to enlarge the monograph to the present volume. However, the general plan has remained the same, and readers acquainted with the monograph will readily find their way here. We continue to lean more heavily than ever on vectors and matrices and to utilize topological notions.


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Издание: 2-nd edition

Год издания: 1962

Количество страниц: 400

Добавлена в каталог: 16.12.2012

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
$\omega$-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 $C^{r}$, 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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