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Ott E. Ч Chaos in dynamical systems
Ott E. Ч Chaos in dynamical systems

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Ќазвание: Chaos in dynamical systems

јвтор: Ott E.

јннотаци€:

This book is an in-depth and broad text on the subject of chaos in dynamical systems. It is intended to serve both as a graduate course text for science and engineering students, and as a reference and introduction to the subject for researchers. Within the past decade scientists, mathematicians and engineers have realized that a large variety of systems exhibit complicated evolution with time. This complicated behaviour, called chaos, occurs so frequently that it has become important for workers in many disciplines to have a good grasp of the fundamentals and basic tools of the emerging science of chaotic dynamics. The author's style is pedagogic, and the book will be of value both as a graduate text and also as a reference work for researchers in science and engineering needing to understand this important new subject. Homework problems are also included throughout the book.


язык: en

–убрика: ‘изика/ƒинамические системы/

—татус предметного указател€: √отов указатель с номерами страниц

ed2k: ed2k stats

√од издани€: 1993

 оличество страниц: 385

ƒобавлена в каталог: 28.09.2005

ќперации: ѕоложить на полку | —копировать ссылку дл€ форума | —копировать ID
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ѕредметный указатель
$D_q$      79
Abrupt bifurcation to chaotic scattering      301
Accessible      295
Action-angle variables      221Ч2
Anderson localization      207 359
Anomalous diffusion      264
Arnold diffusion      257
Arnold tongues      194 266
Attractor      10Ч14
Attractor merging crisis      277
Autonomous Fermi system      243Ч245
BakerТs map      107
Basin boundary (see also fractal basin boundary)      278
Basin boundary metamorphosis      294Ч299
Basin of attraction      33 54
Belousov Ч Zhabotinskn reaction      63Ч64
Bernoulli shift      27
Bernoulli system      261 262
Bifurcation      44
Bifurcation diagram      39
Bifurcation to chaotic scattering      299Ч303
Billiard      258Ч260 335
Binomial coefficient      76
Blinking vortex flow      247
Boundary crisis      277Ч283
Box-Counting Dimension      69Ч75 195
C-system      261Ч262
Cannonical variables      213Ч214
Cantor set      43 65 71Ч74 172 316
Capacity      69
Cat map      128Ч129 257
Center subspace      118
Chaos      2Ч5 132
Chaotic scattering      129 166Ч176 266 299Ч303 360Ч361
Chaotic transient      75 146 151Ч152 266 278 291Ч294
Circle map      189Ч199
Classical limit      334
Conjugate maps      56 67
Conservative      10 12
Constant of the motion      220
Continued fraction      239
Controlling chaos      145Ч148
Correlation dimension      90
Correspondence principle      334
Couette Ч Taylor flow      90Ч92 185Ч186 196Ч197
Crisis      277Ч291
Crisis induced intermittency      283Ч291 303
Critical crisis exponent      279Ч280
Critical point      37
Cumulative density      337
Decay time      328 333
Degrees of freedom      208 209
Delay coordinates      19Ч21 93Ч97
Delay time      17 361
density      31 51 73
Density of states      336Ч338 345Ч351
DevilТs staircase      195
Diffusion      241Ч243 356
Dissipation      11Ч12
Distribution of finite time Lyapunov exponents      322Ч326
Doubling transformation      270
Dripping faucet      4 64
Duffing equation      3
Dynamical systems      6Ч10
Eikonal      252
Elliptic      219 228 232
Embedding      93Ч97
Energy level spacings      339Ч344
Energy level spectra      336Ч351
entropy      138Ч144 310 322Ч323
Ergodic      55 261 262
Ergodic theorem      55
Exterior dimension      98Ч100
Fat fractal      97Ч100 195 228
Final state sensitivity      158Ч161
Finite time Lyapunov exponents      322Ч326
First-order phase transition      see УPhase transitionФ
Floquet form      119
FloquetТs theorem      354
Flow      6
Forced damped pendulum      7 153
Fractal      13
Fractal basin boundary      129 153Ч166 266
Fractal dimension      13 69Ч93
Free energy      310
Frequency locking      191 193 194
Frobenius Ч Peron equation      51
Gaussian orthogonal ensemble (GOE)      341Ч343
Gaussian unitary ensemble (GUE)      341Ч343
Generalized bakerТs map      75Ч78 81Ч86 133 140Ч142 307Ч309 315Ч316 321 332
Generating function      213
Generic bifurcation      45Ч47 266 303
Generic intersection      95 96 230
Geometrical optics      346
Golden mean      199 239
Gram Ч Schmidt orthogonalization      148
Green function      344
Gutzwiller trace formula      see УTrace formulaФ
Harmlton Ч Jacobi equation      223
Harmltonian systems      208Ч265
Hausdorff dimension      100Ч103 313
Helmholtz equation      335 342
Henon map      13 16 17
Heteroclinic intersection      124
Heteroclinic tangency crisis      280Ч1
Homoclinic intersection      124
Homoclinic orbit      292Ч3
Homoclinic tangency crisis      280Ч281
Hopf bifurcation      201Ч202 266 273Ч274 293
Horseshoe      108Ч114 162
Hydrogen atom      356
Hyperbolic      124Ч129 174 219 228 232 301 318
Hyperbolic range      313
Hyperbolic with reflection      219
Ikeda map      278Ч279
Impact parameter      166
Incommensurate      185
Information dimension      79 134 176
Integrable      220Ч224 235
Interior crisis      277 283
Intermittency      272Ч277 303
Intermittent bursting      284
Intermittent switching      284
Internal energy      310
Invariant density      51
Invariant measure      54
Invertible      8Ч9
Involution      220Ч221
Isomorphism      144
Jacobian matrix      115
K-system      261 262
KAM      191 224Ч229 267 303
Kicked double rotor      146Ч147 155Ч156
Kicked rotor      216 254
Lebesgue measure      65
Level repulsion      343Ч344
Limit cycle      11
LiouvilleТs theorem      210Ч211
localization      see УAnderson localizationФ
Localization length      358 359
Logistic map      8 31Ч44 266 268
Lorenz system      57Ч9 189 291Ч294
Lower hybrid wave      253Ч255
Lyapunov dimension      134
Lyapunov exponent      55 129Ч138 176 322Ч326
Lyapunov number      see УLyapunov exponentФ
Lyapunov partition function      316Ч322 327 330Ч331
Magnetic field lines      249Ч251
Magnetoelastic ribbon      289
MAP      7
Measure      31
Metamorphosis      see УBasin boundary metamorphosisФ
Metric entropy      138Ч143 322Ч323
Mixing      256 261 262
Mixing, in fluids      246Ч251
Multifractal      88 305Ч333
Multifractal measure      305
N-frequency quasipenodicity      184Ч185 189 200Ч204 222
N-ton      223
Natural density      31
Natural measure      31 78 326
Noise      92 93 272Ч273 277 290 360
Nonattracting chaotic sets      129 151Ч183
Noninvertible      8Ч9 203
One-dimensional maps      23Ч68 266
Orbit      6
Partition function      327 330Ч331
Pendulum      see УForced damped pendulumФ
Period doubling bifurcation      34Ч36 45 48 273Ч274
Period doubling cascade      37Ч41 238 266Ч272
Period three      39Ч44
Period three window      40
Periodic orbits partition function      327 330Ч331
Periodic orbits sum rule      327 351
Phase transition      267 310Ч313 333
PlanckТs constant      334
Poincare recurrence theorem      214
Poincare surface of section      see УSurface of sectionФ
Poincare Ч Birkhoff theorem      228
Poincare Ч Cartan theorem      212Ч213 222
PoincareТs integral invariant      211
Pointwise dimension      86 306
Poisson distribution      339
Pole placement      146
Power law correlations      264
Power spectra      185Ч186 199Ч200 272 277
Probability measure      53
q-order entropy spectrum      322Ч323
Quantum chaos      334Ч362
Quantum chaotic scattering      360Ч361
Quasipenodicity      184Ч207 266
Random matrices      340Ч342 351
Random walk      264
Ray equations      251Ч252
Rayleigh Ч Benard convection      4 275
Rays      346Ч350
Regular scattering      168
Renormalrzation group      199 240 267Ч272 277 303
Resonant ton      227 229Ч235
Rotation number      188 191 199
Routes to chaos      5
Saddle-focus      294
Saddle-node bifurcation      48 273Ч276
SarkovsknТs theorem      49
Scars      353Ч354
Scattering angle      166
Scattering function      166
SchrodingerТs equation      335 336
Self-similar      72
Semiclassical      334
Shadowing      18 66 126Ч127
Shift      112
Shift of finite type      114
Singularity index      305
Singularity spectrum      305Ч313
Small denominators      191
Spectral rigidity      341Ч342
Stability coefficient      30
Stable      30 17
Stable manifold      122Ч129 153 172 176 278Ч279 281
Stable subspace      118
Stadium billiard      260 353
Standard map      217 235Ч237
Stationary phase      349
StirlingТs approximation      83
Strange Attractor      13 69Ч107
Strange nonchaotic attractor      205
Stream function      246
Subcritical Hopf bifurcation      207 273Ч274
Supercritical Hopf bifurcation      202
Superstable      30 37 268
Surface of negative geodesic curvature      260Ч261
Surface of section      9 10 12
Symbolic dynamics      74 75 108Ч114
Symplectic      209Ч213
Tangent bifurcation      44 45
Tangent space      124
Tangent vector      124
Temperature      310
Tent map      23Ч25
Thermodynamics      309
Three wave coupling      59Ч62
Time delay      170 361
Time reversal symmetry      173 183 339Ч341
Time T map      10 215
Tokamak      249Ч251 255
Topological entropy      138 143Ч144 322Ч323 327
Topologically conjugate      144
Trace formula      344Ч351
Trajectory      6
Transient lifetime      279
Transitive      113
Twist map      230
typical      78
Uncertainty exponent      98 99 159
Unitary      357
Universal      38 39 40 267
Unstable      30 117
Unstable manifold      122Ч129 172 176 281
Unstable subspace      118
Unstable-unstable pair bifurcation      283
Van der Pol equaiion      12
Volume preserving      10
wavefunction      335 352Ч354
Weyl formula      338
Window      40 266 303
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