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Korsch H.J., Jodl H.-J. — Chaos: A Program Collection for the PC
Korsch H.J., Jodl H.-J. — Chaos: A Program Collection for the PC

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Название: Chaos: A Program Collection for the PC

Авторы: Korsch H.J., Jodl H.-J.

Аннотация:

Chaos: A Program Collection for the PC presents an outstanding selection of executable programs with introductory texts to chaos theory and its simulation. Students in physics, mathematics, and engineering will find a thorough introduction to fundamentals and applications in this field. Many numerical experiments and suggestions for further studies help the reader to become familiar with this fascinating topic. The second edition includes one CD-ROM, the executable programs are Windows 95 compatible.


Язык: en

Рубрика: Математика/Численные методы/Моделирование физических процессов/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Издание: 2-nd edition

Год издания: 1998

Количество страниц: 311

Добавлена в каталог: 25.02.2005

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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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 $\sim$)      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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