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Addison P.S. — Fractals and chaos
Addison P.S. — Fractals and chaos

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Название: Fractals and chaos

Автор: Addison P.S.

Аннотация:

The aim of this textbook is to provide the reader with an elementary introduction to fractal geometry and chaotic dynamics: subjects which have attracted immense interest throughout the scientific and engineering disciplines. The book may be used in part or as a whole to form an introductory course in either or both subject areas. A prominent feature of the book is the use of many illustrations to convey the concepts required for comprehension of the subject. Plenty of problems are provided to test understanding. In addition, advanced mathematics is avoided in order to provide a concise treatment and speed the reader through the subject areas.

The book can be used as a text for undergraduate courses or for self-study.


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1997

Количество страниц: 256

Добавлена в каталог: 26.10.2005

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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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, $r, \theta$ 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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