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| Авторизация |
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| Korsch H.J., Jodl H.-J. — Chaos: A Program Collection for the PC |
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| Предметный указатель |
3DISC program 6 7 122 292
Action-angle variables 15 27
Almost periodic 14 15 17 24 26 29 299 305
Analog computer 205 207 210
Anharmonic vibrations 166
Area preserving maps 17 21 28 39 46 70
Arnold tongues 202 299
Attractor 22 163 299
Attractor, Lorenz 2 270
Attractor, Rossler 274
Attractor, strange 24 177 193 227 230 262 271 306
Autonomous system 22 249
Auxiliary equation 264
Baker map 202
Barrier, absolute 148
Basin of attraction 22 170 227 299
Benard convection 2 5 305
Bifurcation 22 24 42 62 80 152 299
Bifurcation for one-dimensional maps 35 187
Bifurcation for two-dimensional maps 38 227 230 243
Bifurcation, diagram 36 38 84 176 185 200 212 214
Bifurcation, Hopf 24 26 43 215 243 257 303
Bifurcation, inverse 192
Bifurcation, Neimark 38 243
Bifurcation, pitchfork 35 42 84 166 190
Bifurcation, tangent 36 42
Billiard program 6 7 52 292
Billiards, analytic 64
Billiards, circle 47 85
Billiards, convex 45
Billiards, elliptical 48 55 56
Billiards, integrable 47 48 50 64
Billiards, stadium 50 55
Billiards, systems 17 29 45
Birkhoff’s symmetry lines 88
Bistability 166
Bouncing ball 4 154 155
Boundary crisis 224
Breathing chaos 87
Burgers map 243
Butterfly effect 16
Cantor set 25 120 129 227 300
Cauchy — Riemann differential equations 227
Caustic 49 64
Cellular automata 5
Chain rule 31 35
Chaos generator 207 249
CHAOSGEN program 6 7 211 292
Chaotic 16 300
Chaotic, band 57
Chaotic, repellor 116 118
Chaotic, scattering 115
Chladni figure 65
Circle, billiard 47 85
Circle, map 202
Coexistence of attractors 24 170 230
Collision, complex 115
Collision, number 117 122
Coloring algorithms 231 235
Commensurable frequencies 15
Conic section 40 41 49
Conservative systems 12 13 18 45 68
Constant of motion 13
Continued fractions 29
Contraction of phase space 22 182 209
Control parameter 12 210 222 260 279 286
Convex billiards 45
Couette — Taylor flow 5
Cremona map 244
Crisis 224
Critical point 200
Critical value 24 26 35 83 151 163 178 218 224
Deflection function 117 122
Degrees of freedom 12 14 300
Delayed logistic map 243
Determinism 60
Deterministic chaos 1 11 300
Deviation matrix 46 61 63 72
Difference equation 12 300
Differential equations 12 91 210 249 300
Discrete dynamical system 12 22 23 37 181 300
Dissipative 301
Dissipative maps 37 182
Dissipative systems 12 22 270 289
Distorted Mandelbrot map 242 245
Divergence 38
Double-pendulum 89
Dpend program 6 7 93 292
Dripping faucet 4 205
Driven rotor 288
Duffing oscillator 2 22 157 210 260
Duffing program 6 7 161 292 301
Dynamical system 12
Eigenfrequency 99
Eigenmode 99 102
Eigenvalue 37 43 65 216
Eigenvector 99
Electronic circuits 6 178 222
Elliptic fixed point 20 28 40 56
Energy surface 14 22
Ergodic 13 22 45 50 58 106 194 301
Euler method 91 210 213
Euler — Lagrange equations 89
Exponential divergence 32 60
Extended phase space 138
Farey tree 202
Feedback 4 5 208 225
Feigbaum program 6 184 292
Feigenbaum, constant 191 219 301
Feigenbaum, diagram 163
Feigenbaum, machine 205
Feigenbaum, scenario 181 218
Fermi acceleration 137 301
Fermi program 6 7 139 292
Fermi-mam model 2 137
Fibonacci numbers 30 109
Fibonacci sequence 301
File-select box 296
Fixed point 47 210 302
Fixed point, elliptic 20 28 40 56
Fixed point, higher order 72 76 86 150
Fixed point, hyperbolic 20 28 42 56 82
Fixed point, hyperbolic with reflection 40 42
Fixed point, stable 20 34 72 147 188
Fixed point, unstable 20 34
Flip 38
Flow 12 14
Flutter 38
Flux tube 265
Focal point 49
Forbidden trajectory 78 135
Fourier transform 223 226 302
Fractal 24 25 131 171 302
Fractal, dimension 24 120 121 133 302
Friction 12 182
Golden mean 30 109 302
Gravitational billiards 64 67 87 88
Gravitational pendulum 174
Hamiltonian, equations of motion 14 240
Hamiltonian, system 12 18 37 39 249 302
Harmonic oscillator, damped and driven 173
Harmonic oscillator, parametrically excited 263
Harmonic response 174
Henon map 242
Henon — Heiles system 2 275 303
Heteroclinic points 21
Heun method 210 213
Hill’s equation 263
Homoclinic points 20
Homoclinic tangle 28
| Hopf bifurcation see “Bifurcation Hopf”
Horseshoe (Smale’s  ) 25 230
Horseshoe map 25
Hyperbolic fixed point 20 28 42 56 82
Hysteresis 170 177 214 219 224
Incomplete symbolic dynamics 135
Information loss 32 198
Initial condition 303
Input of mathematical functions 297
Installing the programs 8 292
Integrable systems 13 14 18 284
Integrable systems, billiards 45
Integral of motion 14 18 49 265 264 284
Integral, equation 32
Intermittency 26 36 42 203 287 303
Invariant curve 17 47 57
Invariant density 32 106 194
Invariant set 303
Invariant torus 15 45 278
Inverse bifurcation 192
Involution, integrals in 14
Irregularity 11 16 50
Ising model 5
Jacobian, determinant 22
Jacobian, matrix 70
Jacobi’s constant 283
Josephson junction 5 287
Julia set 228 237 303
K-system 16
KAM-Theorem 18 27 45 57 87 107 139 144 303
Kepler’s third law 281
Kicked rotator 202
Kicked systems 182
Leapfrog method 92
Lewis invariant 264 265
Liapunov see “Lyapunov”
Lifetime chart 230
Limit, cycle 23 169 303
Limit, point 24
Linear 304
Linearized equations 43 216
Linearized map 32 34 37 46 69 147
Logistic map 183 304
Logistic map in the complex plane 227
Logistic map, basic properties of 187
Logistic map, bifurcation diagram 190 192
Logistic map, period doubling of 190 192
Long-lived trajectories 126 128 134
Lorenz, attractor 2 270
Lorenz, equations 2 270 304
Lyapunov exponent 16 24 31 304
Lyapunov exponent for flows 33
Lyapunov exponent for mappings 31 186 194
Lyapunov exponent for the logistic map 196
Lyapunov exponent for the tent map 197
Lyapunov exponent, computation of 33
Mandelbr program 7 233
Mandelbrot, map 37 183 227
Mandelbrot, set 229 237 240 245 304
Map, area preserving 17 21 28 39 46 70
Map, baker 202
Map, Burgers 243
Map, circle 202
Map, Cremona 244
Map, Henon 242
Map, horseshoe 25
Map, linearized 32 34 37 46 69 147
Map, logistic 183 304
Map, Mandelbrot 37 183 227
Map, one-dimensional 34 181
Map, Poincare 16 22 37 46 68 165 212 252 305
Map, quadratic 184 227 304
Map, quartic 199 284
Map, sin 199 201
Map, standard 151
Map, tent 196
Map, two-dimensional 37 227
Map, Ushiki 244
Markov process 146
Mask menus 295
Mathematical functions 297
Mathematical operations 297
Mathieu equation 263
McCumber parameter 287
Microwave cavity 65
Milne equation 265
Mixing 15 45
Mobius strip 275
Mode locking 202 304
Multiple scattering 115
Multiscale fractals 131 135
Navier — Stokes equation 2
Neimark bifurcation 38 243
Neutral stability 34 62
Newton iteration 52
Noble, number 30
Noble, tori 21 31
Noise 203
Non-convex billiards 56
Noninvertible maps 202
Nonlinear system 3 12 304
Numerical algorithms 91 95 231
Numerical integration 110
Numerical techniques 51 121 161 210 250
ODE program 6 8 293
One-dimensional maps 34 181
Ordinary differential equations 6 249
Oscillator, anharmonic 166 170
Oscillator, Duffing 22 157 260
Oscillator, harmonic 23 157 173 263
Oscillator, Ueda 2 160 171
Oscillator, Van der Pol 2 226 286 306
Paul trap 88
Pendulum 2 89 113 255
Period doubling 186 191 217 223 304
Period doubling, bifurcation 4 175 187
Periodic orbits 15 76 200
Periodic point see “Fixed point”
Perturbed Mandelbrot map 242 245
Phase space 12 305
Phase space, density 55 106
Phase space, subitem organization 14 76 80 86 101 104 143 144
Pitchfork bifurcation 35 42 84 166 190
Poincare — Birkhoff theorem 28 45 58
Poincare, map 16 22 37 46 68 165 212 252 305
Poincare, scenario 26 45
Poincare, section 16 22 250 277 306
Poisson bracket 13
Polygon billiard 64
Population dynamics 37 182 244
Power spectrum 203 223 226 305
Prandtl number 2
Pre-computed examples 293 294
Pre-defined constants 298
Pre-defined functions 297
Predictability 1
Program installation 292
Program, 3DISC program 6 7 122 292
Program, Billiard program 6 7 52 292
Program, CHAOSGEN program 7 211 292
Program, Dpend program 6 7 93 292
Program, Duffing program 6 7 161 292 301
Program, Feigbaum program 6 184 292
Program, Fermi program 6 7 139 292
Program, MANDELBR program 7 233
Program, ODE program 7 8 293
Program, WEDGE program 6 7 73 292
Quadratic form 41
Quadratic map 184 227 304
Quantum, chaos 155 289
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