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| Sparrow C. — The Lorenz equations: bifurcation, chaos, and strange attractors |
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| Предметный указатель |
Almost periodic behaviour 63 64
Attractor 5 9 66 74 103 185 234
Averaging 132—150 259—261
Baroclinic instability 188
Basin of attraction 5 48
Bifurcation 6 7 9 16 20 22 23 39 40 42 50—75 91—93 99 106 107 115 118 139 149 154 161—172 179 183—191 208 210 218—220
Bounded system 5
Branched manifold 44—46 229 230
Cantor set 21 36 37 205 231
Chaotic attractor 5 174 176
Chaotic behaviour 4—7 31 32 36 58 62—75 83 84 110 110 155 159 160 168 174 177 178 190 208 215 217
Characteristic exponent 186
Combinatorics 39 50 104 171—174 244
Contracting foliation 43 44 49 102 208 230
Contraction 9 18 20 35 36 43 49 52 77—81 102 198 205 220 231 261
Cyclic permutation 23 39
Deterministic systems 3
Dissipative systems 4 5 9 100 167 196—198
Divergence 9 198
Fluid convection 1—3
Free group 125
Hamiltonian systems 5
Henon map 70 75
Heteroclinic bifurcation 167—172 176 183
Heteroclinic orbit 127 164—172 188
Homoclinic explosion 12 16 22—24 26 28 32 37—42 44 50 86 90- 100 103—116 121 131 139 140 149 153—166 170—172 176 179 182—185 190 191 199—210 233 239—256
Homoclinic explosion explosion 114 250 251
Homoclinic orbit 12 15 16 20 21 23 37 39 40 42 50 90 91 115 126 133 134 155 156 170 172 191 199—210 228
Homotopy group 125
Hooked return maps 76—92 100—102 109 110 114 236 247
Hopf bifurcation 11 12 25—28 32 38 42 49 107 113 137—140 150 153 158 172 179 186 188 190 235 236
Horseshoe 109 111 209
Intermittent chaos 62—69 74 174
Kneading invariants 226—229
Kneading sequences 101 224—256
Laminar behaviour 62—66
Liapunov functions 9 196—198
Linearization 9 11 12 16 17 20 35 44 47 119 151 153 199 200 211 212 221 236 239
Locally eventually onto, definition 224
Lorenz list, basic 245
Lorenz list, definition 245
Lorenz list, minimal 245
Lorenz list, non-destructive 246
Lorenz, E.N. 1- 3 8 9 32 66 70 194
Maxima-in-z 45 86 101 115—119 130 131 173 175 234—238
Meta-stable chaos 31
Meteorology 1
Models 1 4 188 189 194 195
Monstrous formula 221 222
| Noise 3 186
Noisy periodicity 69—73
Non-destructive sequence, definition 106
Non-stable, definition 193
Non-symmetric definition 8
Non-wandering set 5 6 21 24 49 64 66 81—83 88 91 103 104 110 113 127 130 132 177 193 198 234
One-dimensional interval maps 56 58 64 65 69 70 75 76 100—102 173—176 201—204 208 223—238 251—256
Optics 188
Original, definition 24
Periodic orbits 3 6 8 12 21—28 36—44 47 50—79 82—100 103 106—118 126—190 207 209 212—220 234—256 261
Periodic orbits without extra twisting, definition 155
Poiseville flow 189
Prandtl number 2
Preturbulence 31 32 35 48 235 236
Rayleigh number 2
Recurrent behaviour 5
Return map, definition 17
Rotation, direction of 8 154
Saddle-node bifurcation 52—54 58 59 64—66 74 91 92 100 103 149 164 173 174 182 187 218 219 247 248
Saddles 9
Semi-flow 44—46 229 230 233
Semi-periodicity, definition 70
Sensitive dependence on initial conditions 22 36 208 216 241
Sequences of symbols, definition 37
sinks 9
sources 9
Stable manifold, definitions 193
Stable, definition 193
Stationary points 9
Stiff equations 5
Strange Attractor 5 24 31—49 70 74 76 103 113 190 208 209 223 231—233
Strange invariant set 21—42 48 50 90 92 103 108 113 153 156 162 208—210 236 239—241 247 248
Structural stability 233
Subcritical Hopf bifurcation 11 32
Supercritical Hopf bifurcation 11 186 188
Symmetric definition 8
Symmetry 8 16 20—23 32 42 52—74 100 107 109 119 133 174 187 188 190 201 210 235 252
T-generated, definition 23
T-homoclinic explosion, definition 23
T-homoclinic orbit, definition 22
Thermosolutal convection 188
Torus, invariant 9 55 187 188
Transience 3
Truncation 3 186
Turbulence 3 4 189 208
Type (a), definition 20
Type (b), definition 20
Unstable manifold, definition 193
Unstable, definition 193
Weather 1
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