Электронная библиотека Попечительского совета механико-математического факультета Московского государственного университета
Smith L.A. - Chaos: A Very Short Introduction
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Название: Chaos: A Very Short Introduction
Автор: Smith L.A.
Аннотация: Chaos exists in systems all around us. Even the simplest system can be subject to chaos, denying us accurate predictions of its behavior, and sometimes giving rise to astonishing structures of large-scale order. Here, Leonard Smith shows that we all have an intuitive understanding of chaotic systems. He uses accessible math and physics to explain Chaos Theory, and points to numerous examples in philosophy and literature that illuminate the problems. This book provides a complete understanding of chaotic dynamics, using examples from mathematics, physics, philosophy, and the real world, with an explanation of why chaos is important and how it differs from the idea of randomness. The author's real life applications include the weather forecast, a pendulum, a coin toss, mass transit, politics, and the role of chaos in gambling and the stock market. Chaos represents a prime opportunity for mathematical lay people to finally get a clear understanding of this fascinating concept.
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Рубрика: Физика /
Статус предметного указателя: Готов указатель с номерами страниц
ed2k: ed2k stats
Год издания: 2007
Количество страниц: 180
Добавлена в каталог: 22.05.2008
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Предметный указатель
AC Map 42-43
Accountability 125-126
Accuracy 125-126
Advection models 132-133
Almost every 34 163
Analogue models 133 134
Area-perimeter method 81
Attractors 35-39 45-47 163
Attractors, chaotic 69-71 164
Attractors, Henon 69-71
Attractors, Henon - Heiles 72
Attractors, Lorenz 66 67
Attractors, Moore - Spiegel 67 69-71
Attractors, strange 84-85 168
Auto-Correlation Function (ACF) 88
Babbage, Charles 123
Baker's Apprentice Maps 98 99-101
Baker's Map 98-101
Barometer 6
base two 88-89
Basin of attraction 163
Bayesians 126
Bell-shaped curve 8 9 52 114-115 155
Ben Dahir, Sissa 22-23
Bifurcation diagram 60-62
Binary notation 88-89
Blood cells 71
Borders/boundaries 80
Bradbury, Ray 1 5-6
Brillouin, Leon 104
Burns effect 15 142 146 163
Burns' Day storm 10-16 139-142
Butterfly effect 1 5-6 15 164
Cantor, Georg 77
card tricks 108 108-110
Causation 88
Chaotic attractors 69-71 164
Cheat with the Ace of Diamonds (de la Tour) 19-21
Chess 22-23
Climate modelling 143-146 159-160
Clouds 81
Coastlines 80
Commerce 146-147
computer simulations 34 43-44 90-91 107-110 117-120 135-136
Computers 88-91 107-110
Conservative dynamical systems 164
Correlation 88
Darwin, Charles 4-5
Data assimilation 122
Data-based models 117-120 132-134
De Morgan, A. 76 80
Delay equations 71
Delay reconstruction models 117-120 133 164
Delay-embedding state space 116-120
Determinism 1 3 42 88 90 107 158 164
Digitally periodic loops 107-110
dimensions 65
Dimensions, dimension estimates 115-116
Dissipative chaos 66-71 83
Dissipative dynamical systems 45 164
Doubling time 92-93 101 164
Duration of observations 120
Dynamic noise 55
Dynamical systems 33-35
Dynamical systems, computer simulations 34 43-44 90-91 107-110 117-120 135-136
Dynamical systems, creation of information 89-90
Dynamical systems, mathematical 33-52 89-90
Dynamical systems, physical 33-34 53-57 64 147-149 150-151 157-158
Earth's atmosphere/ocean system 148
Eddington, Arthur 17-18 138 159
Effectively exponential growth 93 164
Electronic circuits 148-149 150-151
Embedology 116-120
Energy sector 147 160
Ensemble forecasts 28-29 102 125-126 138-143 149 150-151 164-165
Ensemble weather prediction systems (EPS) 138-143
Epidemics 71
Errors 4
Errors, exponential growth of 27-28
Errors, forecast errors 29-31 106-107
Errors, observational uncertainty 4 160 166
Errors, representation error 106
European Centre for Mediumrange Weather Forecasts (ECMWF) 138 139-143 142-143
Evolution 5
Exponential growth 22-29 30 165
Exponential-on-average growth 93 94
Fair odds 152
Farmer, J.D. 116
Feigenbaum number 61-64
Fibonacci numbers 26-27
financial markets 146-147
Fitzroy, Robert 5 6 124 132-133
Fixed points 37 60-61 165
flows 65-66 165
Folding 29-32
Forecast errors 29-31 106-107
Forecasting 16 123-131 see
Forecasting weather see Weather forecasting
Forecasting, accuracy and accountability 125-126
Forecasting, ensemble forecasts 28-29 102 125-126 138-143 149 150-151 164-165
Forecasting, model inadequacy 126-127
Forecasting, pandemonium 127-131
Fournier D'Albe, Edmund Edward 77-79
Fournier Universe 78-79 85
Fractal dimensions 80-81 85-86
Fractals 76-86 165
Fractals in physics 79-81
Fractals in state space 81-85
Fractals, solution to Olbers' paradox 77-79
Franklin, Benjamin 3-4
Full Logistic Map 37-39 39-42 88 96-97
Galton Boards 8 9 126-127
Galton, Francis 6-8
Geometric average 95-97 165
Grassberger, Peter 116
Great Storm of 1987 11
Growth, exponential 22-29 30 165
Growth, exponential-on-average 93 94
Growth, linear 23
Growth, stretching, folding and growth of uncertainty 29-32
Hamiltonian chaos 72
Henon attractor 69-71 86
Henon map 69-71 83-84
Henon - Heiles attractor 72
Hide, Raymond 148
Higher-dimensional systems 65-72 74
Higher-dimensional systems, Lyopunov exponents in 97-101
Hokusai, Katsushika 80
Implied probability 152
Indistinguishable state 165
Infinitesimal quantities 31 93-94 102-103 165
Information without correlation 88
Information, computers and 88-91
Information, content 91
Information, mutual 91-92
Integers 104-105
Iterated Function Systems (IFS) 43
Iteration 33 165
Judd, Kevin 115 152
Kepler, Johannes 77
La Tour, Georges De 19-21
Lacunae 85
Lagrangian chaos 65-66
Laplace's demon 3
Laplace, Pierre 3 4
Leading Lyapunov exponent 93
Least squares approach 114-115 155
Leonardo of Pisa 25
Leverrier, Urbain Jean Joseph 6 57 132-133
Limits 113
Linear dynamical systems 10 28 51 156 165
Linear growth 23
Logistic map 45 59-60 92 95 155
Logistic Map, attractors 46 48-49
Logistic Map, computer simulations 107-110
Logistic Map, universality 60-64
Long-range modelling see models
Lorenz attractor 66 67
Lorenz system 66-69 101 157-158
Lorenz, Ed 6 66 74 133 145 148
Lothar/T1 storm of 1999 142-143
Low-dimensional systems 58-64 74
Lyapunov exponents 93-102 157 165-166
Lyapunov exponents in higher dimensions 97-101
Lyapunov exponents, positive exponents with shrinking uncertainties 101-102
Lyapunov time 166
Macbeth 124-125
Mach, E. 53
Machete's Moore - Spiegel circuit 117 118 149 150-151
Mandelbrot, Benoit 80 86
Maps 23 35-44 166 see
Markets 146-147
Mathematical dynamical systems 33-52 89-90
Mathematical dynamical systems, attractors 35-39 45-47
Mathematical dynamical systems, maps 35-44
Mathematical dynamical systems, parameters and model structure 44-45
Mathematical dynamical systems, statistical models of Sun spots 50-52
Mathematical dynamical systems, tuning model parameters and structural stability 47-50
Mathematical fractals 76 77
Mathematical models 15 58-75
Mathematical models, delay equations 71
Mathematical models, dissipative chaos 66-71
Mathematical models, exploiting insights of chaos 73-75
Mathematical models, Hamiltonian chaos 72
Mathematical models, higher-dimensional systems 65-72 74
Mathematical models, origin of mathematical term 'chaos' 65
Mathematical models, universality 60-64
Mathematics 20-21 34 55-56 159
Maximum likelihood 115
Maxwell, James Clerk 8-9
May, Lord 58-60
Medical research 71
Mercury 57
Meteorology see Weather forecasting
Middle Thirds Cantor set 77 85-86
Middle Thirds IFS Map 43 81-83
Model inadequacy 57 111 126-127 130-131 152-153 160
Models 16 27 132-153 166
Models, climate 143-146 159-160
Models, data-based 117-120 132-134
Models, mathematical see Mathematical models
Models, odds and probabilities 149-153
Models, parameters see Parameters
Models, Phynance 146-147
Models, physical systems 147-149 150-151
Models, simulation 135-137
Models, weather forecasting 12-16 135-143
Moore - Spiegel attractor 67 69-71
Moore - Spiegel system 117 118 149 150-151
Moran - Ricker Map 41 59 60 64 95-96
Mutual information 91-92
NAG (Not A Galton) Board 127-131
Neptune 57
New Zealand 143
Newton's Laws 3
Newton, Isaac 73 79
Night sky, darkness of 77-79
Noise 53-54 166
Noise model 54 92 105 111 166
noise reduction 29
Noise, dynamic 55
Noise, exponential error growth 27-28
Noise, observational 4 55-57 92 106 111
Non-constructive proof 46 166
Nonlinearity 1 10 60 155 159-160 166
Nonlinearity, model parameter estimation 114-115
Numbers 104-105 155-156
Numerical weather prediction (NWP) models 135-137
Observational noise 4 55-57 92 106 111
Observational uncertainty 4 8 166
Observations 105-107
Observations and model states 154
Observations, duration of 120
Observations, operational weather forecasting 12-15
Odds 149-153
Olbers' paradox 77-79
Osceledec, V. 93
Packard, N.H. 116
Pandemonium 127-131 166
Parameters 24 166
Parameters and model structure 44-45
Parameters, best values for 113-115 154-155
Parameters, tuning 47-50
Perfect Model Scenario (PMS) 54 56 57 114 122 166
Period doubling 61-64
Periodic loops 43 50 61-64 65 86 167
Periodic loops, attractors 46 48-49
Periodic loops, digitally 107-110
Persistence models 132
Philosophy 20-21 35 53 57 154-161
Philosophy, burden of proof 157-158
Philosophy, complications 154-157
Philosophy, shadowing and the future 159-161
Phynance 146-147
Physical dynamical systems 33-34 53-57 64 157-158
Physical dynamical systems, models and 147-149 150-151
Physical dynamical systems, observations and noise 55-57
Physical fractals 76 77 79-81
Physics 20-21 34 56 159
Planets 57
Poe, Edgar Allen 4 8 77
Poincare section 71 167
Popper, Karl 125-126
Population dynamics 25-29 58-64 105-106
Predictability 16-18 51-52 123-131 167
Predictability, quantifying 91-97 101 see
Prediction Company (PredCo) 146-147
Probabilistic odds 152
probability 129-131 161
Probability, odds and 149-153
Procaccia, Itamar 116
proof 157-158
Proof, non-constructive 46 166
Quadrupling Map 36-37
Quantification 87-103
Quantification, computers and information 88-91
Quantification, dynamics of relevant uncertainties 102-103
Quantification, information without correlation 88
Quantification, Lyapunov exponents 93-102 157 165-166
Quantification, statistics for predicting predictability 91-97
quantum mechanics 54
Quartering Map 37 39 40 45 95
Quincunx see Galton Boards
Rabbit Map 25-29
Random dynamical systems 42-44 54-55 89-90 167
Random number generators 44
Read, Peter 148
Real World 16-18
Real world, models and 147-149 150-151
Real world, science in 19-21
Recurrent trajectory 32 107 158 167
Representation error 106
Rice Map 22-24
Richardson, L.F. 77 79 80-81 135 137
Roulette 133-134 152
Ruelle, David 84
Sample-statistics 113 167
Self-similarity 76-77 78
Sensitive dependence 1-2 5-6 15 94 107 158 167
Shadowing 111 125 156 159-161 167
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