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| Addison P.S. — Fractals and chaos |
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| Предметный указатель |
Antipersistence 65
Attractor 93 119
Attractor, chaotic 93 123
Attractor, periodic 93
Attractor, regions of behaviour 179
Attractor, strange 7 93 123
Autocorrelation function 172
Averaged pointwise dimension 167
Baker map 102
Basin of attraction 96 120 179
Belousov — Zhabotinsky chemical reaction 198
Bifurcation diagram 98
Binary tree 4
Box counting dimension 30 163
Box counting method 30
Broad-band spectrum, chaos 156 158
Broad-band spectrum, noise 158
Brownian landscapes 72
Brownian motion 54 58
Brownian motion,  method 55
Brownian motion, trace of 55
Brownian motion, trajectory 55
Brownian motion, x, y method 55
Buckled beam 195
Butterfly effect 125
Cantor sets 8
Cantor sets, random 27
Central limit theorem 63
Chaos 6 92 125
Chaotic motion 6
Chaotic orbit 92
Characterizing chaos, dimension estimates 164
Characterizing chaos, frequency spectra 156
Characterizing chaos, Lyapunov exponents 159
Characterizing chaos, visual inspection 155
Chua's circuit 198
Circle map 102
Clouds 2
Coastline 2 29
Coastline of Iceland 49
Coastline of mainland Scotland 53
Complex map 106
Connected Julia set 106
Control parameter 89 119
Correlation dimension 164
Coupled oscillators 138
Degrees of freedom 135
Deterministic 6 123
Deterministic nonperiodic flow 6
Diffusing clouds 61
Diffusion 82
Diffusion coefficient 61
Diffusion coefficient, fractal 65
Diffusion Limited Aggregation 79
Diffusion processes 76
Diffusion, anomalous diffusion 65
Diffusion, Brownian 61
Diffusion, Fickian 61
Diffusion, non-Fickian diffusion 65
DIMENSION 3 163 184
Disconnected Julia set 107
Discrete dynamical systems 87
Divider dimension 37
DLA (diffusion limited aggregation) 79 83
Duffing oscillator 119 147
Duffing oscillator, frequency spectra 156
Eckmann — Ruelle limit 183
Embedding dimension 176 186
Euclidean dimension 11
Feigenbaum number 101
Feigenbaum period doubling route to chaos 146
Fern 2
Fine particles 39
Fluid systems 141 149
Folding 132 see
Fourier transforms 156 see
Fractal diffusion coefficient 65
Fractal dimension 3 8
Fractal dimension, false lowering of 79
Fractal dust 26
Fractal models 72 see
Fractal structure of strange attractors 104 129
Fractals 1
Fractals, random 29
Fractals, regular 8
Fractional Brownian motions (fBms) 54 63
Fractional Brownian surfaces 71 83
Frequency spectra 156 184
Fully developed turbulence 143
Gaussian map 102
Gaussian probability distribution 55
Generator 9
Hamiltonian systems 147
Hausdorff dimension 30
Henon map 102
Henon model 102
Hillside silhouette 2
Hurst exponent 61
Hyperchaos in the Roessler model 133
Hypercubes 31
Hypervolumes 31
Hysteresis 146
Information dimension 163
Initiator 9
Intermittency 146
Internal crack surfaces 72 see
Isosets 69 see
Journal bearing 195
Julia set 106
Kaplan — Yorke conjecture 168 see
Koch curve 16
Koch curve, quadratic 19
Koch curve, random 27
Koch island 19
Koch snowflake 19
| Laminar flows 141
Landau model 145
Levy flights 70
Limit cycle attractors 123
Logarithmic spiral 4
Logistic curve 89
Logistic map 88 93
Logistic map, graphical iteration of 93
Lorenz equations 125
Lorenz map 129
Lorenz model 125 148
Lorenz model, power spectra 158
Lyapunov dimension 168
Lyapunov exponents 159 185
Lyapunov spectrum 161
Mandelbrot set 108 112
Manneville — Pomeau intermittent route to chaos 146
Mathematical fractals 4
Menger sponge 23
Method of structured walks 36
Method of structured walks, alternate method 38
Method of structured walks, inswing method 38
Method of structured walks, outswing method 38
Mini-Mandelbrot set 110
Minimum mutual information criterion 173
Minkowski sausage 19
Misiurewicz points 110
Molecular diffusion 54
Motif 9
Multifractals 39
Mutual information 172
Natural fractals 2
Natural landscapes 72 see
Navier — Stokes equations 141
Noise 158 177 186
Noise, black 81
Noise, brown 80
Noise, dynamical 111
Noise, measurement 177
Noise, pink 80
Noise, white 80
Non-invertible map 88
Nonlinear feedback 88
Normal probability distribution 55
Orbit 89
Particle tracking method 77
Perimeter-area relationship 43 46
Period doubling bifurcation 98
Period doubling route 98
Persistence 65
Phase plane 123
Phase portraits 7 123
Phase space 123
Plumes 61
Poincare map 123
Pointwise dimension 167
Population growth 87 see
Post-transient oscillation 119
Power law 80
Power spectral density 80
Power spectrum 84 158
Prefractals 9
Prisoner set 106
Quadratic Koch curve 19
Random walk 63
Rayleigh — Benard convection 125 201
Reconstructon of attractors 170
Reconstructon of attractors, autocorrelation function 172
Reconstructon of attractors, dominant period relationship 172
Reconstructon of attractors, embedding dimension 176
Reconstructon of attractors, method of time delays 170 186
Reconstructon of attractors, minimum mutual information criterion 172
Reconstructon of attractors, visual inspection 172
Regular Brownian motion 54
Reynolds number 142
Richardson plot 37
Ring cavity 202
Roessler system 132 148
Routes to chaos and turbulence 145
Ruelle — Takens route to chaos 145
Scaling region, correlation dimension 166
Self-affinity 61
Self-similarity, exact 3 8
Self-similarity, statistical 2 27
Self-similarity, strict 4
Sensitive dependence on initial conditions 124
Sierpinski carpet 23
Sierpinski gasket 4 23
Similarity dimension 14
Simulated soot particle 39
Sine map 101
Smith limit 183
Snowflake 19
Spatially extended systems 138 141
Strange Attractor 7 93 123
Stretching and folding 132
Structural dimension 39
Structured walk 30 36
Taylor — Couette flow 143 198
Tent map 101
Textural dimension 39
Time delays (method of) 170
Time series 91
Topological dimension 11
topology 11
Traces 55
Trajectories 54 55 123
Transient oscillation 119
Triadic Koch curve 16
Turbulent flows 141
Universality 7
Verhulst model 88
Visual inspection 155
Wall cracks 2
Weak turbulence 143
Zerosets 69
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