Wiggins S. — Chaotic transport in dynamical systems :: Электронная библиотека попечительского совета мехмата МГУ

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Wiggins S. — Chaotic transport in dynamical systems

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Название: Chaotic transport in dynamical systems

Автор: Wiggins S.

Аннотация:

Provides a new and more realistic framework for describing the dynamics of non-linear systems. A number of issues arising in applied dynamical systems from the viewpoint of problems of phase space transport are raised in this monograph. Illustrating phase space transport problems arising in a variety of applications that can be modeled as time-periodic perturbations of planar Hamiltonian systems, the book begins with the study of transport in the associated two-dimensional Poincaré Map. This serves as a starting point for the further motivation of the transport issues through the development of ideas in a non-perturbative framework with generalizations to higher dimensions as well as more general time dependence. A timely and important contribution to those concerned with the applications of mathematics.

Язык:

Рубрика: Физика/Нелинейная динамика, Хаос/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1992

Количество страниц: 301

Добавлена в каталог: 09.10.2005

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Предметный указатель

$S^{2m-1}$       225 230
$S^{2m-1}$ , normally hyperbolic invariant (2m-1)-dimensional sphere      227
$\epsilon$ , exponentially small in      257
Action-angle representation      212
Action-angle variables      78 222 228 256
Annulus      77
Area-preserving      18
Arnold diffusion      212 241 268
Attracting set, time-dependent      179
Attractor      viii 1
Aubry-Mather theory      1
Barriers, partial      193
Beats      159
Beats, homoclinic      159
Behavior, asymptotic      206
Bernoulli shift      55 56 57 60
Bernoulli shift on two symbols      61
Bifurcation theory      122
Boundary conditions, rigid      102 114
Bubble dynamics      10
Cantor set      61 76 185
Cantor set of 1-tori      186
Cantor set of points      186 189
Cantori      7 17 78 81 82 194
Cantori, noble      208
Chaos      ix 54 92 184
Chaos, suppression of      190
Chaotic      57
Chaotic region      98
Codimension one      209
Coefficient of expansion in the direction of $\xi_0$       97
Coherent structures      82 89
Commensurate      159
Conservation laws      33
Convection, steady      114
Convection-diffusion equation      101
Correlations      200
Cray X-MP      117
Cut-off parameter      203
Decay rates      43
Diffusion coefficient      196
Diffusion, infinite      202
Diophantine condition      78
Dissipative term      141
Duffing      168
Duffing oscillator, two-frequency forced      174
Dynamical systems theory      121
Dynamics      1
Dynamics near the resonance      251
Dynamics, one-dimensional      76
Effective diffusivity      102 103
Elliptic      210
Elliptic periodic point      74
Energy surface      209
Energy transfer, intramolecular      vii
Energy, drift in      271
Escape probabilities      61
Fast mixing      202
Flow Control      89
Flux      73 89 108 175
Flux across the roll      103
Flux of species      109
Flux of species       91
Flux of species into region       31
Flux, average      157 158 167
Flux, computation of      157
Flux, instantaneous      156
Flux, local      23
Flux, long time      137
Frequency vector      250
Generating function      75
Geometrical, structures      124
Geometry, pendulum-type      206
Global minimum      76
Golden, mean      132
Guassian probability distribution      116
Hamiltonian      135
Hamiltonian, $\ell$ -resonance      263
Hamiltonian, single resonance      252
Harmonic oscillators      216
Heteroclinic cycle      62 129
Homoclinic coordinates      68
Hopf fibration      216
Hydrodynamic stability      82
Hyperbolicity      18
Hyperbolicity, normal      127 183 222
Implicit function theorem      70
Incommensurate      138 159
Incommensurate frequencies      166
Incompressible      89
Integrable      210
Integrals      211
Interpolate      121 122
Intersections, secondary      204
Invariant circles, nonexistence of      78
Invariant set      58
Invariant set, normally hyperbolic      209 250
Invariant tori, foliation by      211
Involution      211
Irrational rotation      75
Island bands      198
Island chains      194 249
KAM      1
KAM theory      7 76 215 230 236
KAM tori      82 87 117 198 204 212 257
Liapunov characteristic exponent      96
Liapunov characteristic exponent in the direction of $\xi_0$       97
Liapunov exponent      202
Liapunov exponent, time-dependent      97
Liapunov-type numbers, generalized      222
Librational motions      5
Lift      75
Liouville — Arnold theorem      211 217
Lobe area      200
Lobe dynamics      37 42 53 92 119 200
Lobe structures      176
Lobe transport      114
Lobes      20 21 34 35 42 49 72 89 132 133 141 147 150 159 176 239 270
Lobes in $\chi(\theta)$       142
Lobes in the set, number of      146
Lobes of fluid      178
Lobes, families of      148
Lobes, generalization of      247
Manifold, homoclinic      65 255
Manifold, invariant      174
Manifold, orientable, two-dimensional      18
Manifold, primary intersection (pim)      135 136 137 141 142
Manifold, transverse heteroclinic      231 232
Manifold, transverse homoclinic      231 232
Map on the cylinder      205
Map sequence, traveling horseshoe      185
Maps, area-preserving      31 73 223
Maps, bi-infinite sequence of      121 122 124 126 144 173
Maps, extended shift      189
Maps, horseshoe      184
Maps, non-area-preserving      34
Maps, sequences of      121 172
Maps, standard      51
Maps, traveling horseshoe      188
Markov models      193 197 198 200 206 208
Markov processes      197
Melnikov function      233 235 242 247
Melnikov function, quasiperiodic      129 130 132 135 141 142 147 149 159 160
Melnikov’s method      13 64 122
Metric      55
minimizing      76

Mixing infinite      206
Mixing region      87 92 96
Molecular diffusion      81 103 105 111 114 117 119 197
Molecular diffusion coefficient      115
Molecular diffusivity      82
Molecular dissociation      viii
Molecular dissociation, semi-classical study of      171
Morse function      270
Morse oscillator      13 43
Morse oscillator, quasiperiodically forced      171
Moser Twist Theorem      76 77 78
Mutually commensurate      138
Mutually commensurate frequencies      160
Mutually incommensurate      139 221
Nekhoroshev’s theorem      236
Non-area-preserving      18
Nonhyperbolicity      79
Nonresonance      212
Normalization      167
Notational ambiguity      51
Orbit      122
Orbit, critical      4
Orbit, heteroclinic      71 129 130
Orbit, homoclinic      5 7
Orbit, periodic      265
Orbit, quasiperiodic      17 73 75
Orbit, quasiperiodic minimizing      76
Oscillating strain-rate field      176
Oscillating vortex pair (OVP)      38 83 84 167
Oscillating vortex pair (OVP) flow      105 176 179 193 194
Oscillating vortex pair (OVP) lobe structure      177
Oscillation, modes of      260
Partitions      207
Partitions, complete      202
Passive scalar      vii 81 102 108 111 114
Passive scalar, transport of      91
Peclet number      102
Peclet number, chaotic      116
Pendulum      217
Periodic points, saddle-type hyperbolic      18
Perturbations, nonintegrable      216
Phase shift, relative      150
Phase slice method, double      184
Phase slices      122 137 141 157 159 160 185 189
Phase space      30 33
Phase space structure, pendulum-type      254
Phase space transport      43 61 123
Photodissociation of molecules      13
PIM      see "Manifold primary
PIP      see "Point primary
Poincare map      7 14 38 64 67 71 72 81 82 86 87 89 105 122 126 173 204 228 229
Poincare map of a periodically forced pendulum      44
Poincare map, double      184
Poincare section      71 135 144 154 235
Poincare — Birkhoff normal form      74
Point, heteroclinic      19
Point, homoclinic      19
Point, primary intersection (pip)      19 20 21 141 146 157
Poisson bracket      211 233
Quasiperiodic      123
Quasiperiodic functions      123
Rayleigh number      103
Rayleigh — Benard convection      101
Rayleigh — Benard convection, two-dimensional, time-periodic      201
Recurrent      75
Regions      89
Relative scaling factors      167
Relative scaling factors for the frequencies $\omega_i$       131
Resonance      249
Resonance band      202
Resonance channels      260
Resonance junction      266
Resonance, 1:1      44 51 197
Resonance, capture and passage through      9
Resonance, multiple      261
Resonance, orbit-orbit      9
Resonance, single      250 260
Resonance, spin-orbit      9
Resonant module      262
Rotation number      75
Rotation number of an orbit      75
Rotational motions      5
Runge — Kutta code, fourth-order      117
Sensitive dependence on initial conditions      54 56 62
Separatrix      204 209 210 213
Shift map      56
signatures      114
Signatures of the heteroclinic tangle      111
Signed measure of the distance      71
Singular perturbation      102
Smale horseshoe map      57
Smale horseshoes      81 82 92
Smale — Birkhoff homoclinic theorem      59 62 122
Species      89
Species       30
Spiral, ( $\ell-1$ )-dimensional      137
Stability, islands of      194 197
Stagnation points      104
Stochastic regime      194
Stochastic regions      96 194 195 196 197 206
Stochastic subregions      202
Streamlines      85
Stretch, total      99
Stretching      92
Structural mechanics      viii
Systems near integrable      269
Systems, autonomous      124
Systems, dissapative      271
Systems, nonautonomous      124 172 173
Systems, periodically adiabatically forced      204 206
Three-tori      266
Time dependence, quasiperiodic      121
Topologically conjugate      60
Topologically transverse      21
Toral pims      141 187
Torus, k-dimensional      211
Torus, KAM      212
Torus, normally hyperbolic invariant      125 126 127
Torus, whiskered      212
Tracer      198
Transition probabilities      196
Transition rates      200
Transport      17 121 218
Transport in the phase slices $\chi(\theta)$       14
Transport near resonance      249
Transport of a given species      190
Transport rates      203
Transport surface      142 174
Transport theory      122 173
Transport, barriers to      209 251
Transport, roll-to-roll      105 114 197 198
Transversal intersections      68
Trial-and-error      184
Turnstile      17 23 24 31 53 108 145 146 172 175 181 196 206 239 249 270
Turnstile dynamics      40 44 50 61
Turnstile lobes      30 161 171
Turnstile, multilobe      147
Turnstile, self-intersecting      27 204
Turnstile, time-dependent      175
Twist map      74
Two-dimensional map theory      135
Two-tori      265
Universal cover of the cylinder      74
Vector fields, nonautonomous      143
Vector fields, quasiperiodic      128 184
Vortices, elliptical      2

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