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Электронная библиотека Попечительского совета
механико-математического факультета
Московского государственного университета
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| Mullin T. - The nature of chaos |
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| Предметный указатель |
A/D converter 24
Accessible orbit 211
Arnol'd cat maps 299-300
Attraction, basin of 202-204
Attractor xi-xii
Attractor, Lorenz 222-223
Attractor, reconstruction of xii-xvi 27-34
Attractor, strange xi 19
Attractor, Vallis 246
Attractor, weather 226
Australian blowflies 186
Autocorrelation function 26-27
Baroclinic waves 256
Basin erosion 214
Basin of attraction xii 202-204
Benjamin 82
Berry's semiclassical theory 293-299 305
Bifurcation 11-13
Bifurcation diagram 12 137
Bifurcation, chaotic saddle 213
Bifurcation, codimension-1 56-57
Bifurcation, codimension-2 58 206
Bifurcation, flip 204
Bifurcation, fold 53
Bifurcation, Hopf 55
Bifurcation, local mode 264-266
Bifurcation, pitchfork 16 52
Bifurcation, saddle-node 109
Bifurcation, subcritical 14
Bifurcation, supercritical 13
Bifurcation, symmetry breaking 98
Billiards 286-287
Birkhoff 98
Bootstrapping 306
Capacity dimension 45-50
Capsize of ships 218-220
Cardiac rhythms 183
Cat maps 299-300
Chaotic saddle, bifurcation 213
Chaotic saddle, catastrophe 211
Chaotic transient 144 210
Chicken pox 171
Codimension 56
Codimension-2 bifurcation 206
Codimension-2 point 58
Congenital rubella syndrome 180
Control parameters 9 54-55 75
Correlation dimension 46-48 158
Coulomb forces 275-276
Coupled difference equations 138-139
Crisis 204
Cycle, heteroclinic 6
Cycle, limit xii 14
Cycle, Milankovitch 250
Cyclonic 'bombs' 258
Damping 6-7
Daphnia populations 185
Delay differential equation 144
Delays, method of 27-34
Density of states 288
Deterministic chaos x-xi 85-91
Difference equations, coupled 138-139
Difference equations, exponential 105
Difference equations, quadratic 103
DIMENSION 20
Dimension, capacity 45
Dimension, correlation 46-48 158
Dimension, fractal 21
Discrete Fourier Transform 26
Doubling, period 16-17
Dover cliff phenomenon 116
Dynamical diseases 183-185
Dynamical systems theory 95
EEG pa, terns 184
Eigenvalue 194
El Nino 241
Elastica 51
Embedding dimension 156
Energy balance climate model 249
Engineering integrity 216
Environmental stochasticity 187
Equations, delay-differential 144
Equations, difference 99
Equations, Euler strut 51
Equations, logistic difference 103
Equations, Lorecz's 223
Equations, Mackey - Glass 145
Equations, Mathieu's 9
Equations, Navier - Stokes 69
Equations, ordinary differential 3
Equations, partial differential 70
Equations, Rossler 19
Equatorial waves 238
Equilibrium point 4
Escape scenario 202
Euler strut 51 98
Exponential map 105
Exponents, Lyapunov 42-45 122-123
Fast Fourier Transform 26
Feigenbaum cascade 204
FGGE 235
Fixed point xi 5
Fixed point, map 103
Fixed point, stable 6 103
Fixed point, unstable 6 103
Flip bifurcation 204
Folding 110-111
Forecasting 155-156
Fourier spectrum xiii 28-30
Fourier transform 25-26
Fractal, basin boundaries 214-16
Fractal, boundary 201 211
Fractal, dimension 21
Fractal, fingers 216
Fractals in control space 220
Frequency locking 88
Frequency-dependent natural selection 132-138
Gaussian orthogonal ensemble 285
Gaussian unitary ensemble 285
Global atmospheric research programme (GARP) 235
Golden mean 273
Grassberger - Procaccia 158
Gutzwiller trace formula 290-291
Hamiltonian systems, Poincare maps 261-264
harmonic oscillator 3
Harmonics xiii 26-27
Heteroclinic cycles 6
Hilltop saddle cycle 207
HIV/AIDS 194-198
Homoclinic connection 61-62
Homoclinic orbit 61 91
Homoclinic tangle 211 269-271
Hopf bifurcation 55
Host-parasitoid systems 141
Host-pathogen interactions 178
Hydrodynamic stability 71-73
Hydrogen atom 275-276
Hyperchaotic 144
Hysteresis 14
Ice ages 249-250
Imperfection 53
Incursive fractal 215
Insect populations 188
Instability 10
Intermittency 91
International Whaling Commission - (IWC) 138
Intraseasonal oscillation 234-236
Islands of stability 274
Iterated map 101-103
Julia 98
| KAM curves 274
Kelvin wave 238 248
Landau 73
Langford 88
Laplace 97
Length of day (LOD) 235
Limit cycle xii 14
Limit point 59
Linearized system ix
Logistic map 103
Lorenz 98-99
Lorenz attractor 222-223
Lyapunov exponents, experimental determination 42-45
Lyapunov exponents, one-dimensional maps 122-124
Lyapunov exponents, two-dimensional maps 144
Lyapunov stability 98
Mackey - Glass equation 145
Magnetic fields 275-276
Mandelbrot 98
Maps, antisymmetric 125-130
Maps, cat 295-300
Maps, coupled 138-144
Maps, cubic 127
Maps, delayed logistic 141
Maps, exponential 105
Maps, iterated 101-103
Maps, logistic 103
Maps, Poincare 33-41 102 261-264
Maps, quadratic 103
Maps, return 38
Maps, tent 153
Maps, two-dimensional 138
Marine plankton 172
Mathieu's equation 9
May 99
Measles, data 158-164
Measles, spatial dynamics 164-171
Method of delays 27-34
Milankovitch cycles 250
Multiplicities xvi 15 83-84
Navier - Stokes' equations 69-71
Newton ix 120
Noise 24-25 29
Nonlinear pendulum 3
Nonlinearity 2
Normal mode oscillator 265-266
Number variance 284 297
Numerical bifurcation 14-15
Numerical weather prediction 227-231
Odlyzko 304
Orbit, heteroclinic 6
Orbit, homoclinic 61 91
Orbit, planetary ix
oscillations 3
Oscillations, clamped 6
Oscillations, intraseasonal 234-236
Oscillations, parametrically excited 8
Oscillations, quasi-biennial 236
Oscillations, simple harmonic 3
Oscillations, southern 243
Palaeoclimatology 249
Parametrically excited pendulum 8-20
Pendulum, simple 2
Period doubling 16 99
Phase bottleneck 272-273
Phase plane 3-5
Phase portrait 3-5
Phase portrait, reconstruction 26-38
Phase space 4-8
Pitchfork bifurcation 13
Planetary orbits ix
Poincare 97
Poincare maps 38-40 102
Poincare maps, Hamiltonian systems 261-264
Poincare sampling 38 201
Points, equilibrium 4
Points, fixed xi 5
Points, limit 59
Points, saddle 59
Population dynamics 101 188-192
Population genetics 192
Power spectrum 25-26
Predator prey systems 173
Predictability 7 28-30
Prediction 153-154
Preturbulence 144
Primary resonance 204
Quadratic map 103
Quantum chaology 283
quantum mechanics 282-283
Quasi-biennial oscillation 236
Repeller 7
Resonance 9 266-267
Resonant tongue 10
Return map 38
Return map, stroboscopic 39
Reynolds number 70
Riemann's Zeta-function 392-393
Rossby wave 248
Rossler equations 19
Rotating annulus 254
Ruelle 99
Ruelle - Takens route to chaos 73-74
Saddle focus 62
Saddle point 59
Saddle-node bifurcation 109
Saltzmann 222 249
Semiclassical Berry's theory 293-299 305
Semiclassical limit 282-283
Semiclassical sum rule 295
Sensitive dependence on initial conditions 19-21 120-121 224
Separatrix 6 269
Silnikov 60-67
simple harmonic motion 3
simple pendulum 2-8
Simplex projection 150
Singular value decomposition 34-36
Sloping convection 255
Smale 99
Southern oscillation 243
Spectrum, Fourier xiii 28-30
Spectrum, power 25-26
Stadium problem 275 292
Strange Attractor xi 19
Stretching 19
Subcritical bifurcation 14-15
Supercritical Pitchfork bifurcation 13
Symmetry-breaking 16 51-52 81-83 98
Systems, dynamical 96
Systems, Hamiltonian 261
Systems, predator-prey 173
Takens 99
Taylor vortex 74-76
Taylor - Couette flew 74-91
Taylor, G.I. 81
Teleconnections 231-234
Tent map 153
Three-body problem ix 120
Time series 23-25 149
Time-delayed logistic equation 139-141
Torus xii 38-41
Trajectory matrix 34
Transient 18 144 210
Transition to turbulence 71-73
Turbulence 93
Universal constants (Feigenbaum) 114
Universality 113-117 284-285
Unstable fixed point 6 103
Unstable solution 13
Vallis attractor 246
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