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Lorenz E.N. — Essence of Chaos
Lorenz E.N. — Essence of Chaos



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Íàçâàíèå: Essence of Chaos

Àâòîð: Lorenz E.N.

Àííîòàöèÿ:

Chaos Surrounds us. Seemingly random events - the flapping of a flag, a storm-driven wave striking the shore, a pinball's path - often appear to have no order, no rational pattern. Explicating the theory of chaos and the consequences of its principal findings - that actual, precise rules may govern such apparently random behavior - has been a major part of the work of Edward N. Lorenz. In The Essence of Chaos, Lorenz presents to the general reader the features of this "new science," with its far-reaching implications for much of modern life, from weather prediction to philosophy, and he describes its considerable impact on emerging scientific fields. Unlike the phenomena dealt with in relativity theory and quantum mechanics, systems that are now described as "chaotic" can be observed without telescopes or microscopes. They range from the simplest happenings, such as the falling of a leaf, to the most complex processes, like the fluctuations of climate. Each process that qualifies, however, has certain quantifiable characteristics: how it unfolds depends very sensitively upon its present state, so that, even though it is not random, it seems to be. Lorenz uses examples from everyday life, and simple calculations, to show how the essential nature of chaotic systems can be understood. In order to expedite this task, he has constructed a mathematical model of a board sliding down a ski slope as his primary illustrative example. With this model as his base, he explains various chaotic phenomena, including some associated concepts such as strange attractors and bifurcations. As a meteorologist, Lorenz initially became interested in the field of chaos because of its implications for weather forecasting. In a chapter ranging through the history of weather prediction and meteorology to a brief picture of our current understanding of climate, he introduces many of the researchers who conceived the experiments and theories, and he describes his own initial encounter with


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Ñòàòóñ ïðåäìåòíîãî óêàçàòåëÿ: Ãîòîâ óêàçàòåëü ñ íîìåðàìè ñòðàíèö

ed2k: ed2k stats

Ãîä èçäàíèÿ: 1996

Êîëè÷åñòâî ñòðàíèö: 240

Äîáàâëåíà â êàòàëîã: 14.05.2008

Îïåðàöèè: Ïîëîæèòü íà ïîëêó | Ñêîïèðîâàòü ññûëêó äëÿ ôîðóìà | Ñêîïèðîâàòü ID
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Ïðåäìåòíûé óêàçàòåëü
Adams, John Couch (1819-1892)      113
Almost-periodicity: absence of, and chaos      19—20 142
Almost-periodicity: in Hamiltonian systems      65 67 67
Almost-periodicity: meaning of      18—19
Analogues      85—86
Arrhythmias      15—16 127 149
Asymptotic solutions      118 199
Atmosphere as dynamical system      78 79.
Attracting sets: determination of points on      59—60 60.
Attracting sets: meaning of      59
Attractors: absence of, in Hamiltonian systems      61—62
Attractors: determination of points on      43—45 44 53
Attractors: graphical representation of      41—43
Attractors: in dishpan experiments      89—91
Attractors: meaning of      39—41
Attractors: multiple      55
Attractors: of board model      53—55 54 197—198 198
Attractors: of global weather system      50 97 98 99—100 130
Attractors: of sled model      45—48 46 47 49 197 198
Attractors: of specially designed systems      153 155 155—156 156 157 186 187
Bamsley, Michael Fielding      173
Baseballs      111—112
Basin boundaries: in board model      55—59 56
Basin boundaries: meaning of      55
Basins of attraction: in board model      55—59 74
Basins of attraction: meaning of      55
Bernoulli shifts      204
Bifurcations: in board model      70—76 72 73 75 76 147
Bifurcations: in dishpan experiments      89 147
Bifurcations: in logistic equation      194
Bifurcations: meaning of      69
Bifurcations: period-doubling      71 72 73 74—76 76
Bifurcations: resulting from stability changes      69—70
Bifurcations: saddlenode      70
Birkhoff's "bad" curves      121—124 122 123
Birkhoff, George David (1884-1944)      121 122 123 124 125 127 128 142
Bjerknes, Vilhelm Friman Koren (1862-1950)      95
Board model: attractor of      54 177 197—198 198
Board model: basin boundaries in      55—59 56
Board model: bifurcations in      70—76 72 73 75 76
Board model: detection of chaos in      32 33 34 35—37 36
Board model: determination of attractor of      53—54
Board model: formulation of      26—32
Bradbury, Ray      15
Brahms, Johannes (1833-1897)      150
Business cycles      149 151
Butterfly attractor      14 15 139—141 140 141 145 146 150 177 188
Butterfly effect      14--15 181—184
Butterfues: as symbols of chaos      13—15
Butterfues: as weather modifiers      85 153 181—183
Cantor sets      50 53 176—177 178 194 204
Cantor, Georg (1845-1918)      50
Capacity      168 196
Card shuffling      7 9
Cartwnght — Littlewood attractor      124 124—125 167
Cartwnght, Dame Mary Lucy      123
Cellular automata      174—175
Chaos: "make your own"      151—157 152 153 154 155 See
Chaos: acquisition of technical meaning      20—21 120
Chaos: and atmospheric predictability      102 103—106 142—143
Chaos: awareness of      113—114 120—121 125 128—129 146—147
Chaos: detection of      16 20 25—26
Chaos: in dishpan experiments      89 92
Chaos: in global circulation models      95 102
Chaos: in the atmosphere      79 86 94 108—109
Chaos: meanings of      3—4
Chaos: perceived as randomness      118—119 157—159
Chaos: recognition of, by Poincare      118—120
Chaos: refinements of technical meanings      5—6 7 8 23—24
Chaos: routes to and from      69—70
Chaos: symbols of      13—15
Chaos: technical meaning of, in this volume      4
Chaotic seas      64 66—68 68 147
Charney, Jule Gregory (1917-1981)      98 100 103 104 142
Chirikov, Bons      48 53 191
Climate, S.      50 79
Cloud physics      84. See also Clouds; Rain; Snow
Clouds      81—89 passim
Coefficient of function      28 39 189—190
coin tossing      6—7 9 12 14
Compactness: meaning of      16—17
Compactness: of board model      35 37
Compactness: of global weather system      82 85—86
Compactness: significance of      18—20
Complete randomness      7—8
complexity      4 163 164 165 166 166 167 170
Computation, manual      114 117 128
Computer graphics      43 185
Computers: and awareness of chaos      128—129.See also LGP-3O computer
Computers: and weather forecasting      82 95 98—106
Computers: as equation solvers      26 28 32 114 131 156 157 171
Conservative systems      61. See also Hamiltonian systems
Convection      137 143 145 148
Cross sections      43—56 passim. See also Double cross sections; Poincare sections
Cusps      56 57—58 59
Damping time      28 30
Day, length of      78 94
Determinism      7 8 9 157 159
Devaney, Robert      194
Dewey, Thomas Edmund (1902-1971)      77
Difference equations: as basis for dynamical systems      127. See also Logistic equation; Mappings; Population dynamics
Difference equations: derived from differential equations      13 47—48 121
Difference equations: meaning of      12
Differential equations: as basis for dynamical systems      121 142.
Differential equations: general solutions      111—112 117 139
Differential equations: in sled model      47
Differential equations: meaning of      13
Differential equations: solution curves      117—118
Dimensionality      168—177 passim 178 196—198
Discontinuous mappings      151—152
Dishpan experiments: apparatus for      87—89 88 90 92
Dishpan experiments: flow patterns in      89—92 90 91 93 94 95
Dishpan experiments: implications of      92—94
Disk dynamos      148
Dissipative systems: atmosphere and ocean as      78
Dissipative systems: meaning of      51
Dissipative systems: versus Hamiltonian systems      65 67
Double cross sections      56—57 58—59
Doubling times      104—106 182—183
Doubly asymptotic solutions      118 199
Duffing oscillator      167
Dynamic meteorology      82—87 passim 95 130
Dynamical systems: families of      28 See
Dynamical systems: meaning of      8
Economy      149
Ellipses: as attractors      42 61
Ellipses: as images of circles      50—53 52
Ellipses: as planetary orbits      112 114
Ellipsoids, as images of spheres      55 195—196
Energy      57 62—64 68 99
Equations: of dynamical systems      12—13
Equations: of global weather system      95—96 98.
Equilibrium      22—23. See also Stable equilibrium; Unstable equilibrium
Errors: in weather forecasting      104 105 106 182—184
Errors: in weather observations      85 96—104 136 182—183
European Centre for Medium Range Weather Forecasts      101—102
European Centre model      101—102 104—105
Faller, Alan Judson      92 145
Families of systems      28 62 69
Feigenbaum, Mitchell Jay      194
Filtered equations      99 100 104 132
Flags, flapping, as chaotic systems      5 16 17 20 24
Flows: mappings derived from      13 47—48 121.
Flows: meaning of      13
Fractal leaves      173 176 177
Fractal trees      171—173 172 174 175
Fractal triangles      169 170 170—171 173—174
Fractality      4 169—178 170 171 178. Fractal
Franklin, Philip (1898-1965)      142
Free will      158 159—160
Friction: in board model      27 28 57 74
Friction: in dissipative systems      51
Friction: in pendulums      5 61
Friction: in pinball machine      10 17
Friction: in real sliding systems      152. See also Coefficient of friction; Damping time
Fronts      92
Full chaos: in Birkhoff and Cartwright — Littlewood systems      122—125
Full chaos: meaning of      21—22
Full chaos: recognition of by Poincare      118—119
Full chaos: versus limited chaos      126—127
Fultz, Dave      87 89 92
Gleick, James      4 14 15 21 179
Global Atmospheric Research Program      80 103 110 142—143 181 184
Global circulation models      99—105 passim 109—110 142—143
Global weather system      80—82 85
Golfballs      16—17 112
Graphics      43 185
graphs      18 37—38 41
Gravity, force of: in atmosphere      86 93
Gravity, force of: in dishpan experiments      86 87
Gravity, force of: in ski-slope model      28
Gravity, force of: in solar system      111 113
Guckenheimer, John      49
Haken, Hermann      148
Hamilton, Sir William Rowan (1805-1863)      61
Hamiltonian board model: chaotic seas and islands in      64 65 65—68 67 68
Hamiltonian board model: detection of chaos in      63 64—65
Hamiltonian board model: formulation of      62—64
Hamiltonian systems: as atmospheric models      99
Hamiltonian systems: chaos and periodicity in      64—68 116
Hamiltonian systems: Lyapunov exponents of      195. See also Hamiltonian board model; Standard map; Volume-preserving systems
Hamiltonian systems: meaning of      61—62
Hausdorff dimension      168
Hausdorff, Felix (1868-1942)      168
Heartbeat      15—16 24 127 149
Hide, Raymond      89 90 91 92
High pressure systems      82 83 96—97
Hill's reduced problem      114—117 115 116 133 192—193
Hill, George William (1838-1914)      114 116
Homoclinicity      118 199—204
Horseshoe mappings      125—126 126 127 156 202—204
Howard, Louis Norberg      143
Humidity      80—81 101 105
Initialization      100 102
Instrumentation      84
Invariant sets      59 123—124
Invertible mappings      153
Izrailev, Felix      48 53
Jacobi integral      193
Japanese attractor      165 167
Jet streams      82 89 92—93 100 105
Jupiter      112
Kaplan — Yorke dimension      196
Kaplan, James      196
Keefe, Douglas      150
Knot theory      38 146 147
Kolmogorov, Andrei Nikolaevich (1903-1987)      168
Krakatau      106—107
Krishnamurti, Ruby      143
Kutta, Wilhelm (1867-1944)      185
Laboratory models      26 86—87 See
Laplace, Pierre Simon de (1749-1827)      159
Lasers      148
Leaves, falling, as chaotic systems      5 158
Length of day      78 94
LeVerrier, Urbain Jean Joseph (1811-1877)      113
LGP-3O computer      132—136 137
Li, lien Yien      20—21 120 145
Limited chaos: in Birkhoff and Cartwright-Littlewood systems      122—125
Limited chaos: in horseshoe mapping      125—126 204
Limited chaos: meaning of      21—22
Limited chaos: recognition of, by Poincare      118
Limited chaos: versus full chaos      126—127
Linear predichon      130—134
Linearity      161—162
Littlewood, John Edensor (1885-1977)      123
Lockett, Carolyn      150
Logistic equation      80 147—148 194—195
Lorenz attractor      See Butterfly attractor
Lorenz equahons      188 See
Lorenz, Edward Norton      14—15 69 128 130 136 150—151.
Low pressure systems      82 83 92 96—97 98
Lyapunov exponents      177 195—197
Lyapunov numbers      195 197
Lyapunov stability      142
Lyapunov, Aleksandr Mikhailovich (1857-1918)      142
Malkus, Willem van Rensselaer      143
Malone, Thomas Francis      130 137
Mandelbrot set      163—165 164 167 195
Mandelbrot, Benoit      169 170 173 177
Manifolds: as components of attractors      48 196
Manifolds: stable and unstable      99—202 200 201 203 203—204
Many-body problem      111
Mappings: as generators of chaos      151 153—157
Mappings: derived from flows      13 47—48 121
Mappings: discontinuous      151—153
Mappings: meaning of      12
Mappings: noninvertible      151 156 157 186 See
Markov, Andrei Andreevich (1856-1922)      142
Markov, Andrei Andreevich (son of A.A.M.)      142
Massachusetts Institute of Technology      130 137 142 143
Mathematical models, as approximations      5—6 10 17—18 27—28 35 45 87 95 112.
May, Robert McCredie      147 148
Menlees, Philip      15
Models      See Laboratory models; Mathematical models
Molecules      120
Monte Carlo forecasting      102—103 106
Moon      79
MUSIC      149—150
Nahonal Meteorological Center      102
Nemytskii, Viktor Vladimirovich      142
Neptune      111 113 114
Newton's Laws      26—27 82 111 148 149 189
Newton's method      187—188
Newton, Sir Isaac      111
Noninvertible flows      152—153
Noninvertible mappings      151 157 156 186
Nonlinearity      4 161—163
Numerical integration      96 112 185—188
Numerical weather prediction      95—106 passim 131
Orbits, in phase space      42 117
Orbits, planetary      111—116 passim 128
Oscillations, in atmosphere      96—102 passim. See also Quasi-biennial oscillation
Oscillators: Duffing      167
Oscillators: van der Pol      123
Parabolas      111—112
Parameterizahon      10
Pencils, standing, as unstable systems      22 119
Pendulums      4 5 39 42—43 51 61 162
Period doubling: in board model      71 72 73 74—76 76
Period doubling: in logistic equation      194
Period doubling: meaning of      71
Period doubling: prevalence of      71
Periodicity: absence of, and chaos      18—20 26 35—37 133 136 142
Periodicity: bifurcation to and from      71—74
Periodicity: hypothetical, in atmosphere      108—110 See
Periodicity: in atmosphere      86
Periodicity: in dishpan experiments      90—91
Periodicity: in Hamiltonian systems      67—68 115—116
Periodicity: introduced by Poincare      117
Periodicity: meaning of      18—19
Periodicity: of pendulum      42—43
Periodicity: of ski-slope model      43—44 46—47
Perturbation method      112—113
Phase space, meaning of      41—42
Phillips, Norman Alton      100 139
Pinball machines: as dynamical systems      9—10 13
Pinball machines: chaotic behavior in      10 11 12 18 19 20 62
Pinball machines: elongated      17—18 19 20
Platzman, George William      99
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