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Murdock J. — Perturbations: Theory and Methods |
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Предметный указатель |
Adiabatic invariance of action 439 446 455 460
Airy function 411 457
Almost periodic function 258
Amol'd tongue see Resonance horn
Analytic function 466
Anatomy, human 60 97 322 383
Approximation: asymptotic 68 72
Approximation: one-term, two-term, etc. 34 359
Approximation: order of see Order
Approximation: zeroth, first, second, etc. see Order
Asymptotic see Approximation; Series; Uniformity
Attractor 320
Autonomous 488
Averaging 228 275
Averaging, first order 264 275
Averaging, higher order 243 315
Averaging, justification of 276 281 318
Averaging, relation to multiple scales 228 273
Averaging, stroboscopic 287 317
Bessel funclion 411 457
Bifurcation 15 18 94 129
Bifurcation diagram 18
Bifurcation, Hopf 176 224 415
Bifurcation, limit point see Bifurcation pair
Bifurcation, pair 19 25 129 306
Bifurcation, pair, of limit cycles 185
Bifurcation, pitchfork 39 80 129 132
Bifurcation, saddle-node 18 306
Bifurcation, tangent see Bifurcation pair
Bifurcation, transcritical 44 129 132
Bootstrapping 145
Boundary layer problem 343 417
Boundary value problem 86 115 135 417 479
Brainwashing 84
Canard 407 413 416
Catastrophe 79 213
Characteristic (length, time, etc.) see Dimensional analysts
Common part 365 376
Compact set 468
Comparison equation 381 387
Composite solution 358 362 376 378
Connection problem 459
Conservative 164
Continuation 25 27
Convex set 496
Correction layer condition 377
Correction method 344 376 400 422
Critical problem 185 187 197
Damping 345
Damping, critical, overcritical, undercritical 86
Damping, strong, weak 86 92 144
Degenerate 19 49 55
Degenerate boundary value problem 88
Degenerate nearly 21 24 50 194
Determining equation 180 197 199 297
Detuning 196 262
Differential equation: second order 477
Differential equation: system of 148 480 485
Differential inequality 142. See also Gronwall's inequality
Diffusion-reaction problem 92 104
Dilation see Rescaled coordinate
Dimensional analysis 89 96 346
Discontinuous solution 398 409 413
Dissipation see Damping
Dream 45 136
Duffing equation: derivation of 90 99
Duffing equation: forced 186 202 262 302 308
Duffing equation: free (unforced) 114 168 174 261 292
Dynamical systems 224 323
Eigenvalue 122 441
Eigenvalue, large 448
Eigenvalue, nonlinear 121
Elastica 94
Elbow neighborhood 322
Energy 164
Entrainment 187 189 196 198 225
Entrainment, domain see Resonance horn
Entrainment, index 189 196
Equilibrium point see Rest point
Error see also Remainder
Error estimation 30 135 163 266 281 381 449
Error factor 444 450
Existence: importance of 12 17
Existence: of periodic solutions 170 180 199 293
Existence: of solutions to boundary value problems 87 115 137 418 479
Existence: of solutions to initial value problems 84 479 485
Expanding interval 163
expansion see also Limit process expansion: Series operator
Expansion, operator: inner, outer 359 364
Expansion, operator: intermediate 372
Expansion, operator: middle 393
Exponentially small see Transcendentally small
Extension theorem 375 416
Fast angle 332
First return map see Poincare map
Flow property 488
Fluid flow 425
Forcing frequency 187
Formal: order 13 66
Formal: power series 12
Formal: reasoning 8
Formal: solution 13
Fredholm: alternative 223
Fredholm: integral equation 484
Free frequency 187
Friction see Damping
Gauge function 33 65. gauges
Gauge function, distinguished 36
Gauge function, significant 37
Green's function: for ordinary differential equations 137 484
Green's function: for partial differential equations 133
Gronwall's inequality 143 152 267 291 384
Guiding: center 288
Guiding: system 286 316 319
Heuristic 8
Hill's equation 277
honesty 438
Hooke's law 90 345
Hyperbolic 320
Implicit: differentiation 470 471
Implicit: function theorem 26 469
Impulse (initial momentum) 344
In-track error 174 242
Initial layer problem 343
Initial value problem 84 106 140 227 343 479 485
Inner-outer solution 362
Inner: equation 349 420
Inner: expansion operator 359 364
Inner: layer 351 356
Inner: solution 349
Inner: variable 359 420
Integral: equation 137 141 384 453 483
Integral: inequality 138 141 267 384
Intermediate variable 372
Internal layer problem 344
Irrational number 190
Jungle 7
Kernel 141 484.
Kolmogorov — Amol'd — Moser (KAM) theory 332
Langer transformation 458
Least period 188
Level curve 166
Lie transform 339
Limit cycle 176 406. solution
Limit process expansion 75 352 374
Lindstedt method 157
Linearization 489
Lion 7 150
Liouville — Green transformation 450
Lipschitz constant 495
| Logic 497
Matching 344
Matching by intermediate variable 371
Matching by Van Dyke's roles 358 419
Matching derivatives 392
matching rules (IVMR) 373
Mathieu equation 186 202 277
Matrix: exponential of 150
Matrix: norm of see Norm
Method of see individual heading (e.g.for method of averaging see
Molasses, influenced by position of earth in orbit about sun 426
Multiple scales 216 227
Multiple scales for initial and boundary layers 377. See also Correction method
Multiple scales, first order method 233
Multiple scales, higher order methods 230 242
Multiple scales, justification of 238
Multiple scales, relation to averaging 228 273
Near-identity transformation 283
Nearly linear see Nonlinear weakly
Negation 501
Noncritical problem 185
Nondegenerate 12 49
Nondegenerate, boundary value problem 88 115 120
Nondimensional see Dimensional analysis
Nonlinear: strongly 95
Nonlinear: weakly 84 86 101
Nonoscillatory 85 120 418 435
Nonsense 61 68
Nonstandard analysis 407
Nonuniformity see Uniformity
Norm: Euclidean 150 495
Norm: matrix 150 152 154
Norm: operator 152
Norm: vector 154 495
Orbit 166 178 187 397 480 488
Orbital error 173
Order: asymptotic 29 61 68
Order: formal 13
Order: leading 34
Order: of magnitude 60 61 68
Order: zeroth, first, second, etc. 34 228 229 288 289
Oscillation 85 406. solution
Oscillation, relaxation 406
Oscillation, self-sustained 176
Oscillator 85
Oscillator, coupled 257 342
Oscillator, nearly linear 86 144
Oscillatory see Nonoscillatory
Outer-inner solution 362
Outer: equation 350 420
Outer: expansion operator 359 364
Outer: layer 351
Outer: solution 350
Overlap: condition 353 357 372 390
Overlap: domain 374
Overlap: failure of 391
Overlap: rigorous 375
PARAMETER 64
Parameter, bifurcation 18 129
Parameter, control 49 64
Parameter, large 429 434
Parameter, natural 6 62 91 121 346
Parameter, perturbation 4 49 64 91 121 347
Parametric excitation 277
Patching method 344 351 415
Period map 188 197 287 490.
Periodic: regime 168 437
Periodic: solution 159 166 176 180 199 297
Periodic: standard form see Standard form periodic
Perturbation: family 4 62 91 121
Perturbation: family, viewed as a path 6 62
Perturbation: parameter see Parameter perturbation
Perturbation: regular 73
Perturbation: series see Series perturbation
Perturbation: singular 73
Phase plane 166 396
Poincare map 179 188 197.
Pointwise 67
Potential see Energy
Potential well 166 437
Quantifier 497
quantum mechanics 436 459
Quasiperiodic function 258
Rational number 190
recycling 146
Reduced problem 4 6 55 344 398 435
Remainder 16 23 146 464.
Repellor 320
Rescaled: coordinate 46 55 95 346 348 391 394 435
Rescaled: parameter 55 412
Residual 23 146 382
Resonance 187 191 195
Resonance, complete 332
Resonance, harmonic 197 254 261
Resonance, horn (or tongue) 193 212
Resonance, internal 329
Resonance, near 193
Resonance, subharmonic 197 215 259
Resonance, superharmonic 197
Resonance, surface 335
Resonant 187 191 195
Resonant, nearly 193
Rest point 166 170 488
Reynolds number 7 426
Riccati equation 442
Richness 56 428
Root 4
Root, unbounded 43 48
Running away inequality 150 291
Saddle 320
Salt 210
SCALE see also Multiple scales; Rescaled
Scale, distinguished 56
Schroedinger equation 437
Secular terms 158 235
Secular terms, -secular terms 217 236 248
Separatrix 168
Series: asymptotic 69 72
Series: asymptotic power 72 75
Series: asymptotic, addition of 74
Series: asymptotic, differentiation of 76
Series: asymptotic, integration of 78
Series: asymptotic, multiplication of 75 78
Series: asymptotic, uniqueness of 74
Series: convergent 72 466
Series: formal power 12
Series: Fourier 124 172 182 237 286 491
Series: Fourier, multiple 326 493
Series: fractional power 46 75
Series: generalized asymptotic 73 158 161 216 233
Series: Lindstedt 161 171
Series: ordinary asymptotic 74
Series: perturbation 74
Series: Poincare 74
Series: Puiseux see Series fractional
Series: Taylor 466
Shadowing 323
shooting 88 115 117 184 197
Singular point see Rest point
Sink 320
Slow curve 396
Slow curve, hypothesis of stability for 397 403
Slow curve, hypothesis of stability for, failure of 408
Slow time 161 229
Small denominators (divisors) 328 330 339
Source 320
Stability (including asymptotic, orbital, etc.): of limit cycle 180
Stability (including asymptotic, orbital, etc.): of linear system 486
Stability (including asymptotic, orbital, etc.): of periodic solution 193 293 301
Stability (including asymptotic, orbital, etc.): of rest point 489
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