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Hirsch M.W., Smale S. — Differential Equations, Dynamical Systems, and Linear Algebra
Hirsch M.W., Smale S. — Differential Equations, Dynamical Systems, and Linear Algebra

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Название: Differential Equations, Dynamical Systems, and Linear Algebra

Авторы: Hirsch M.W., Smale S.

Аннотация:

This book is about dynamical aspects of ordinary differential equations and the relations between dynamical systems and certain fields outside pure mathematics. A prominent role is played by the structure theory of linear operators on finite-dimensional vector spaces; the authors have included a self-contained treatment of that subject.


Язык: en

Рубрика: Математика/Анализ/Дифференциальные уравнения/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1974

Количество страниц: 338

Добавлена в каталог: 09.04.2005

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
$C^1,C^2$      178
$nil(x)$      334
$\alpha$ Limit point      198 239
$\omega$ Limit point      198 239
Absolute convergence      80
Adjoint      230
Adjoint of operator      206
Andronov      314
angular momentum      21
Annulus      247
Antisymmetric map      290
Areal velocity      22
Asymptotic period      277
Asymptotic stability      145 180 186
Asymptotically stable periodic solution      276
Asymptotically stable sink      280
Autonomous equation      160
Bad vertices      269
Based vector      10
Basic functions      140
Basic regions      267
Basin      190
Basis      34
Basis of solutions      139
Belongs to eigenvector      42
Bifurcation      227 255
Bifurcation of behavior      272
Bifurcation point      3
Bilinearity      75
Boundary      229
Branches      229 211
Brayton — Moser theorem      234
Brouwer fixed point theorem      253
Canonical forms      122 123 331
Capacitance      232
capacitors      211 232
Cartesian product of vector spaces      42
Cartesian space      10
Cauchy sequence      76
Cauchy's inequality      75
Cayley — Hamilton theorem      115
Center      95
Central force fields      19
Chain rule      17 178
Change of bases      36
Change of coordinates      6 36
Characteristic      213 232
Characteristic polynomial      43 103
Closed orbit      248
Closed subset      76
Companion matrix      139
Comparison Test      80
Competing species      265
Complex Cartesian space      62
Complex eigenvalues      43 55
complex numbers      323
Complex vector space      62 63
Complexification of operator      65
Complexification of vector spaces      64
Configuration space      287
Conjugate momentum      293
Conjugate of complex number      323
Conjugation      64
Conservation of angular momentum      21
Conservation of energy      18 292
Conservative force field      17
Continuous map      76
Continuously differentiable map      16
Contracting map theorem      286
Contraction      145
Convergence      76
Convex set      164
Coordinate system      36
coordinates      34
Cross product      20
Current      211
Current states      212 229
Curve      3 10
Cyclic subspace      334
Cyclic vector      334
Dense set      154
Derivative      11 178
Determinants      39 324
Diagonal form      7
Diagonal matrix      45
Diagonalizability      45
Diffeomorphism      242
Differentiation operator      142
Direct sum      41
Discrete dynamical system      278 280
Discrete flow      279
Discriminant      96
Distance      10 76
Dual basis      205
Dual space      36
Dual vector space      204
Dynamical system      5 6 159 160
Eccentricity      26
Eigenspace      110
Eigenvalue      63
Eigenvector      42 63
Elementary $\lambda$-block      127
Elementary Jordan matrix      127
Elementary nilpotent block      122
Energy      18 289
Entire orbit      195
Equation of limited growth      257
Equilibrium      145
Equilibrium point      180
Equilibrium state      145 181
Euclidean three space      287
expansion      149
Exponent (exp)      83
Exponential      74
Exponential approach      181
Exponential of operator      82
Exponential series      83
Factorial      83
Field of force      15
Fixed point      181 279
Flow      6 175
Flow box      243
Focus      93
Force field      16 17 23
Fundamental theorem      162
Fundamental theorem of algebra      328
Fundamental theory      160
Generalized eigenspace      110
Generalized momenta      292
Generic property      154
Genericity      188
Global section      247
Good vertices      269
Gradient      17
Gradient system      199
Graph of map      339
Gronwall's inequality      169
Growth rate      256
Hamilton's equations      291
Hamiltonian      291 293
Hamiltonian vector field      291
Harmonic motion      59
harmonic oscillator      15 105
Higher order linear equations      138
Higher order systems      102
Homeomorphism      312
Homogeneous linear systems      89
Hopf bifurcation      227
Hyperbolic closed orbit      311
Hyperbolic equilibrium      187
Hyperbolic flow      150
Hyperplane      242
identity map      322
Image      34 322
Implicit function theorem      338
Improper node      93
In phase trajectories      278
Independent set (subset)      34
Inductance      213 232
Inductors      211 213 232
Infinite series      86
Initial condition      2 162
Initial value problem      2
Inner product      16 75
integral      23
Invariance      198
Inverse      33
Inverse function theorem      337
Invertibility      33
Isomorphism      35
Iteration scheme      168
Jordan $\lambda$-block      127
Jordan curve theorem      254
Jordan form      127
Jordan Matrix      127
KCl      211 229
Kepler problem      58
Kepler's first law      23
Kernel      33
kinetic energy      18 288
Kirchhoff's current law      211
KVL      212 230
Lagrange's theorem      194
Latus rectum      26
Legendre transformation      292
Length      10 76
Level surface      195 200
Liapunov      192
Liapunov function      193
Liapunov's theorem      180
Lienard's equation      210 215
Limit cycle      250
Limit set      239
Limiting population      257
Linear contraction      279
Linear flow      97
Linear graph      229
Linear map      30 33
Linear part      181
Linear subspace      33
Linear transformation      5
Linearity properties      30
Linearly independent elements      326
Liouville's formula      278
Lipschitz constant      163
Lipschitz function      163
Local section      242 278
Locally Lipschitz      163
Manifolds      232 319
Matrices (matrix)      8 11
Maxwell      191
Minimal set      241
Mixed potential      233
Monotone along trajectory      244
Multiplicity      110
Multiplicity of a root      330
n-body problem      287
Neighborhood      76 305
Newton's equations      289
Newton's second law      15
Newtonian gravitational field      24
Nilpotent      112 117
Nilpotent canonical form      122
nodes      93 211 229
Non homogeneous      99
Nonautonomous differential equations      99 296
Nonautonomous perturbation      308
Nondegenerate bilinear form      290
Nonlinear sink      182
Norm      77
Ohm's law      213
One-form      205
Onto mapping      322
Open set      76 153
Operator      30 33
Orbits      5
Order of differential equation      22
Ordinary boundary points      268
Oriented branch      229
Origin      10
Orthonormal basis      206
Parallelogram law      81
PARAMETER      2
Parametrized differential equation      227
Partial sums      80
Passive resistor      217
Peixoto      314
Pendulum      183
Periodic attractor      278
Periodic solutions      95
Perturbation      304
Phase portrait      4
Phase space      292
Physical states      213 232
Physical trajectory      234
Picard iteration      177
Poincare map      278 281
Poincare — Bendixson theorem      239 248
Pontryagin      314
Positive definiteness      75
Positive invariance      195
potential energy      17 288
Power      231
Predator-prey equation      259
Primary decomposition theorem      110
Product of matrices      32
Proper subspace      33
Rank      41
Real canonical form      130
Real distinct eigenvalues      46
Real eigenvalue      42
Real logarithm of operator      132
Recurrent point      248
Regular point      200
Residual sets (subsets)      158
resistors      211 213
Restriction      322
RLC circuit      211
Saddle      92
Saddle point      190
Scalars      33
Section map      221
Self-adjoint operator      207
Semisimplicity      63 65 116 117
Separation of variables      261
Separatrices      272
SEQUENCE      76
Series      80
Similar matrices      39
simple harmonic motion      59
Simple mechanical system      289
Singularity point      181
Sink      145 180 181 280
Social phenomena      257
Solution of differential equation      161
Solution space      35
Source      95 149 190
Space derivative      300
Space derivative of states      22
Space derivative of unrestricted states      231
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