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Smith L.A. Ч Chaos: A Very Short Introduction
Smith L.A. Ч Chaos: A Very Short Introduction

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Ќазвание: Chaos: A Very Short Introduction

јвтор: Smith L.A.


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.

язык: en

–убрика: ‘изика/

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

ed2k: ed2k stats

√од издани€: 2007

 оличество страниц: 180

ƒобавлена в каталог: 22.05.2008

ќперации: ѕоложить на полку | —копировать ссылку дл€ форума | —копировать ID
ѕредметный указатель
AC Map      42Ч43
Accountability      125Ч126
Accuracy      125Ч126
Advection models      132Ч133
Almost every      34 163
Analogue models      133 134
Area-perimeter method      81
Attractors      35Ч39 45Ч47 163
Attractors, chaotic      69Ч71 164
Attractors, Henon      69Ч71
Attractors, Henon Ч Heiles      72
Attractors, Lorenz      66 67
Attractors, Moore Ч Spiegel      67 69Ч71
Attractors, strange      84Ч85 168
Auto-Correlation Function (ACF)      88
Babbage, Charles      123
Baker's Apprentice Maps      98 99Ч101
Baker's Map      98Ч101
Barometer      6
base two      88Ч89
Basin of attraction      163
Bayesians      126
Bell-shaped curve      8 9 52 114Ч115 155
Ben Dahir, Sissa      22Ч23
Bifurcation diagram      60Ч62
Binary notation      88Ч89
Blood cells      71
Borders/boundaries      80
Bradbury, Ray      1 5Ч6
Brillouin, Leon      104
Burns effect      15 142 146 163
Burns' Day storm      10Ч16 139Ч142
Butterfly effect      1 5Ч6 15 164
Cantor, Georg      77
card tricks      108 108Ч110
Causation      88
Chaotic attractors      69Ч71 164
Cheat with the Ace of Diamonds (de la Tour)      19Ч21
Chess      22Ч23
Climate modelling      143Ч146 159Ч160
Clouds      81
Coastlines      80
Commerce      146Ч147
computer simulations      34 43Ч44 90Ч91 107Ч110 117Ч120 135Ч136
Computers      88Ч91 107Ч110
Conservative dynamical systems      164
Correlation      88
Darwin, Charles      4Ч5
Data assimilation      122
Data-based models      117Ч120 132Ч134
De Morgan, A.      76 80
Delay equations      71
Delay reconstruction models      117Ч120 133 164
Delay-embedding state space      116Ч120
Determinism      1 3 42 88 90 107 158 164
Digitally periodic loops      107Ч110
dimensions      65
Dimensions, dimension estimates      115Ч116
Dissipative chaos      66Ч71 83
Dissipative dynamical systems      45 164
Doubling time      92Ч93 101 164
Duration of observations      120
Dynamic noise      55
Dynamical systems      33Ч35
Dynamical systems, computer simulations      34 43Ч44 90Ч91 107Ч110 117Ч120 135Ч136
Dynamical systems, creation of information      89Ч90
Dynamical systems, mathematical      33Ч52 89Ч90
Dynamical systems, physical      33Ч34 53Ч57 64 147Ч149 150Ч151 157Ч158
Earth's atmosphere/ocean system      148
Eddington, Arthur      17Ч18 138 159
Effectively exponential growth      93 164
Electronic circuits      148Ч149 150Ч151
Embedology      116Ч120
Energy sector      147 160
Ensemble forecasts      28Ч29 102 125Ч126 138Ч143 149 150Ч151 164Ч165
Ensemble weather prediction systems (EPS)      138Ч143
Epidemics      71
Errors      4
Errors, exponential growth of      27Ч28
Errors, forecast errors      29Ч31 106Ч107
Errors, observational uncertainty      4 160 166
Errors, representation error      106
European Centre for Mediumrange Weather Forecasts (ECMWF)      138 139Ч143 142Ч143
Evolution      5
Exponential growth      22Ч29 30 165
Exponential-on-average growth      93 94
Fair odds      152
Farmer, J.D.      116
Feigenbaum number      61Ч64
Fibonacci numbers      26Ч27
financial markets      146Ч147
Fitzroy, Robert      5 6 124 132Ч133
Fixed points      37 60Ч61 165
flows      65Ч66 165
Folding      29Ч32
Forecast errors      29Ч31 106Ч107
Forecasting      16 123Ч131 see
Forecasting weather      see Weather forecasting
Forecasting, accuracy and accountability      125Ч126
Forecasting, ensemble forecasts      28Ч29 102 125Ч126 138Ч143 149 150Ч151 164Ч165
Forecasting, model inadequacy      126Ч127
Forecasting, pandemonium      127Ч131
Fournier D'Albe, Edmund Edward      77Ч79
Fournier Universe      78Ч79 85
Fractal dimensions      80Ч81 85Ч86
Fractals      76Ч86 165
Fractals in physics      79Ч81
Fractals in state space      81Ч85
Fractals, solution to Olbers' paradox      77Ч79
Franklin, Benjamin      3Ч4
Full Logistic Map      37Ч39 39Ч42 88 96Ч97
Galton Boards      8 9 126Ч127
Galton, Francis      6Ч8
Geometric average      95Ч97 165
Grassberger, Peter      116
Great Storm of 1987      11
Growth, exponential      22Ч29 30 165
Growth, exponential-on-average      93 94
Growth, linear      23
Growth, stretching, folding and growth of uncertainty      29Ч32
Hamiltonian chaos      72
Henon attractor      69Ч71 86
Henon map      69Ч71 83Ч84
Henon Ч Heiles attractor      72
Hide, Raymond      148
Higher-dimensional systems      65Ч72 74
Higher-dimensional systems, Lyopunov exponents in      97Ч101
Hokusai, Katsushika      80
Implied probability      152
Indistinguishable state      165
Infinitesimal quantities      31 93Ч94 102Ч103 165
Information without correlation      88
Information, computers and      88Ч91
Information, content      91
Information, mutual      91Ч92
Integers      104Ч105
Iterated Function Systems (IFS)      43
Iteration      33 165
Judd, Kevin      115 152
Kepler, Johannes      77
La Tour, Georges De      19Ч21
Lacunae      85
Lagrangian chaos      65Ч66
Laplace's demon      3
Laplace, Pierre      3 4
Leading Lyapunov exponent      93
Least squares approach      114Ч115 155
Leonardo of Pisa      25
Leverrier, Urbain Jean Joseph      6 57 132Ч133
Limits      113
Linear dynamical systems      10 28 51 156 165
Linear growth      23
Logistic map      45 59Ч60 92 95 155
Logistic Map, attractors      46 48Ч49
Logistic Map, computer simulations      107Ч110
Logistic Map, universality      60Ч64
Long-range modelling      see models
Lorenz attractor      66 67
Lorenz system      66Ч69 101 157Ч158
Lorenz, Ed      6 66 74 133 145 148
Lothar/T1 storm of 1999      142Ч143
Low-dimensional systems      58Ч64 74
Lyapunov exponents      93Ч102 157 165Ч166
Lyapunov exponents in higher dimensions      97Ч101
Lyapunov exponents, positive exponents with shrinking uncertainties      101Ч102
Lyapunov time      166
Macbeth      124Ч125
Mach, E.      53
Machete's Moore Ч Spiegel circuit      117 118 149 150Ч151
Mandelbrot, Benoit      80 86
Maps      23 35Ч44 166 see
Markets      146Ч147
Mathematical dynamical systems      33Ч52 89Ч90
Mathematical dynamical systems, attractors      35Ч39 45Ч47
Mathematical dynamical systems, maps      35Ч44
Mathematical dynamical systems, parameters and model structure      44Ч45
Mathematical dynamical systems, statistical models of Sun spots      50Ч52
Mathematical dynamical systems, tuning model parameters and structural stability      47Ч50
Mathematical fractals      76 77
Mathematical models      15 58Ч75
Mathematical models, delay equations      71
Mathematical models, dissipative chaos      66Ч71
Mathematical models, exploiting insights of chaos      73Ч75
Mathematical models, Hamiltonian chaos      72
Mathematical models, higher-dimensional systems      65Ч72 74
Mathematical models, origin of mathematical term 'chaos'      65
Mathematical models, universality      60Ч64
Mathematics      20Ч21 34 55Ч56 159
Maximum likelihood      115
Maxwell, James Clerk      8Ч9
May, Lord      58Ч60
Medical research      71
Mercury      57
Meteorology      see Weather forecasting
Middle Thirds Cantor set      77 85Ч86
Middle Thirds IFS Map      43 81Ч83
Model inadequacy      57 111 126Ч127 130Ч131 152Ч153 160
Models      16 27 132Ч153 166
Models, climate      143Ч146 159Ч160
Models, data-based      117Ч120 132Ч134
Models, mathematical      see Mathematical models
Models, odds and probabilities      149Ч153
Models, parameters      see Parameters
Models, Phynance      146Ч147
Models, physical systems      147Ч149 150Ч151
Models, simulation      135Ч137
Models, weather forecasting      12Ч16 135Ч143
Moore Ч Spiegel attractor      67 69Ч71
Moore Ч Spiegel system      117 118 149 150Ч151
Moran Ч Ricker Map      41 59 60 64 95Ч96
Mutual information      91Ч92
NAG (Not A Galton) Board      127Ч131
Neptune      57
New Zealand      143
Newton's Laws      3
Newton, Isaac      73 79
Night sky, darkness of      77Ч79
Noise      53Ч54 166
Noise model      54 92 105 111 166
noise reduction      29
Noise, dynamic      55
Noise, exponential error growth      27Ч28
Noise, observational      4 55Ч57 92 106 111
Non-constructive proof      46 166
Nonlinearity      1 10 60 155 159Ч160 166
Nonlinearity, model parameter estimation      114Ч115
Numbers      104Ч105 155Ч156
Numerical weather prediction (NWP) models      135Ч137
Observational noise      4 55Ч57 92 106 111
Observational uncertainty      4 8 166
Observations      105Ч107
Observations and model states      154
Observations, duration of      120
Observations, operational weather forecasting      12Ч15
Odds      149Ч153
Olbers' paradox      77Ч79
Osceledec, V.      93
Packard, N.H.      116
Pandemonium      127Ч131 166
Parameters      24 166
Parameters and model structure      44Ч45
Parameters, best values for      113Ч115 154Ч155
Parameters, tuning      47Ч50
Perfect Model Scenario (PMS)      54 56 57 114 122 166
Period doubling      61Ч64
Periodic loops      43 50 61Ч64 65 86 167
Periodic loops, attractors      46 48Ч49
Periodic loops, digitally      107Ч110
Persistence models      132
Philosophy      20Ч21 35 53 57 154Ч161
Philosophy, burden of proof      157Ч158
Philosophy, complications      154Ч157
Philosophy, shadowing and the future      159Ч161
Phynance      146Ч147
Physical dynamical systems      33Ч34 53Ч57 64 157Ч158
Physical dynamical systems, models and      147Ч149 150Ч151
Physical dynamical systems, observations and noise      55Ч57
Physical fractals      76 77 79Ч81
Physics      20Ч21 34 56 159
Planets      57
Poe, Edgar Allen      4 8 77
Poincare section      71 167
Popper, Karl      125Ч126
Population dynamics      25Ч29 58Ч64 105Ч106
Predictability      16Ч18 51Ч52 123Ч131 167
Predictability, quantifying      91Ч97 101 see
Prediction Company (PredCo)      146Ч147
Probabilistic odds      152
probability      129Ч131 161
Probability, odds and      149Ч153
Procaccia, Itamar      116
proof      157Ч158
Proof, non-constructive      46 166
Quadrupling Map      36Ч37
Quantification      87Ч103
Quantification, computers and information      88Ч91
Quantification, dynamics of relevant uncertainties      102Ч103
Quantification, information without correlation      88
Quantification, Lyapunov exponents      93Ч102 157 165Ч166
Quantification, statistics for predicting predictability      91Ч97
quantum mechanics      54
Quartering Map      37 39 40 45 95
Quincunx      see Galton Boards
Rabbit Map      25Ч29
Random dynamical systems      42Ч44 54Ч55 89Ч90 167
Random number generators      44
Read, Peter      148
Real World      16Ч18
Real world, models and      147Ч149 150Ч151
Real world, science in      19Ч21
Recurrent trajectory      32 107 158 167
Representation error      106
Rice Map      22Ч24
Richardson, L.F.      77 79 80Ч81 135 137
Roulette      133Ч134 152
Ruelle, David      84
Sample-statistics      113 167
Self-similarity      76Ч77 78
Sensitive dependence      1Ч2 5Ч6 15 94 107 158 167
Shadowing      111 125 156 159Ч161 167
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