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| Àâòîðèçàöèÿ |
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| Ïîèñê ïî óêàçàòåëÿì |
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| Tabor M. — Chaos and Integrability in Nonlinear Dynamics: An Introduction |
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| Ïðåäìåòíûé óêàçàòåëü |
Number theory, and properties of frequency 109—112
Oscillator, cubic 19—20
Oscillator, damped linear 5—6
Oscillator, Duffing 35 36
Oscillator, nonautonomous 33—36
Oscillator, quartic 19
Oscillator, simple harmonic 1—3
Overlapping resonances, basic idea of 156—157
Overlapping resonances, for standard map 162—163
Overlapping resonances, method of 154—163
Painleve property, and auto-Backlund transformations 355
Painleve property, and integrability 347
Painleve property, and Lax pairs 355
Painleve property, for ordinary differential equations 330 337—342
Painleve property, for partial differential equations 350—355
Painleve transcendents, first and second 37 286
Painleve transcendents, third 309
Painleve, Paul 327
Parabolic fixed points 138 see
Pendulum, and method of overlapping resonances 160—161
Pendulum, period of 13
Pendulum, phase portrait of 15
Pendulum, separatrix of 16—17
Pendulum, solution in terms of elliptic functions 11—12
Period doubling, basic mechanism of 216—220
Period doubling, bifurcation diagram of 220—222
Period doubling, in area-preserving maps 225
Period doubling, universality of 215 220
Period of oscillation 4
Period three orbits 221 224
Perturbation expansions, and secular terms 94—95
Perturbation expansions, for first-order ordinary differential equation 92—94
Perturbation expansions, for Hamilton — Jacobi equation see “Canonical perturbation theory”
Perturbation expansions, for second-order ordinary differential equation 94—96
Perturbation expansions, regular 90—91
Perturbation expansions, singular 91—92
Phase portrait 14
Phase portrait, for conservative systems 17—20
Phase portrait, of pendulum 15—17
Phase space, of Hamiltonian systems 52
Phase space, symplectic structure of 47 52 81—88
Phase volume, preservation of, and Liouville's theorem 52 56—57
Phase volume, preservation of, differential geometry of 55 88
Phase volume, preservation of, under canonical transformations 55—56
Phase, curve 14
Phase, flow 14
Phase, plane 13
Pitchfork bifurcations 225
Poincare invariants 55 88
Poincare — Birkhoff fixed-point theorem 139—142
Poincare — Cartan invariant, and surface of section 183—184
Poincare — Cartan invariant, as differentia] 1-form 61 84
Poincare — Hopf theorem 71
Point transformations 55
Point vortices 191
Poiseuille flow 195
Poisson brackets, for KdV equation 315
Poisson brackets, in Hamiltonian mechanics 53—54
Poisson distribution, of energy level spacings 244
Poisson sum formula 266
Power spectra, and correspondence principle 241—242
Power spectra, for classical trajectories 152—154
Power spectra, of fluid dynamical experiments 193—194
Psi-series 331 334—335
Quadrature, integration by 2
Quantum maps, closed orbit quantization of 268—272
Quantum maps, evolution of 258—263
Quantum maps, formulation of 256—258
Quantum maps, propagators for 266—268
Quartic NLS equation 318
Quasi-energy spectrum 265
Quasiperiodic orbits 77
Radiation, in nonlinear evolution equations 303
Rayleigh number 205
Rayleigh — Benard convection, experimental observation of 194—195
Rayleigh — Benard convection, Lorenz model of 204—206
Recursion relations 330
Reduction of order, of ordinary differential equations 3
Reflection coefficient 294 see
Regular perturbation expansions see “Perturbution expansions”
Regular spectrum, definition of 240
Regular spectrum, general properties of eigenfunctions 246—254
Regular spectrum, generul properties of eigenvalues 240—246
Residue, of periodic orbits 166 269
Resonances see also “Overlapping resonances”
Resonances, illustration of 155
Resonances, in analytic structure analysis 330
Resonances, in simple oscillators 35
Reynolds number 188
Riccati equation 31 33
Roessler attractor 212
Ruelle — Takens theory 199—202
Russell, John Scott 279
Saddle-node bifurcation 225
Scattering data 291—292
Scattering data, evolution of 297—299
Schwarzian derivative 220
Secular terms, in perturbation theory 95
Self-focusing singularities 317—318
| Semiclassical limit, as a singular limit 229
Semiclassical limit, for time-dependent problems 228—230
Semiclassical limit, for time-independent problems 230—232
Semiclassical wavepackets 238—239
Sensitivity to initial conditions 34
Sensitivity to perturbation, of energy levels 242—243
Separable systems 69—70
Separatrix 16
Separatrix, for pendulum 16—17
Separatrix, in cubic and quartic oscillators 19—20
Separatrix, stable and stable manifolds of 143
Shock formation 284
Similarity solutions, for KdV equation 285
Similarity solutions, for mKdV equation 305
Similarity solutions, for Sine — Gordon equation 309
Sine — Gordon equation, inverse scattering transform for 310
Sine — Gordon equation, simple properties of 305—309
Sine — Gordon equation, with damping and driving 319
Singular manifolds 351—352
Singular perturbation expansions see “Perturbation expansions”
Singularity structure, and integrability 39 see
Singularity structure, and Kovalevskaya 324—327
Singularity structure, of nonintegrable systems 348—350
Smale horseshoe 201—202
Small divisors, problem of 102—104
sn function 9
Soliton, first observation of 279
Soliton, numerical discovery of 280—281
Soliton, theory of see “Inverse scattering transform (IST)”
Spatial correlations, of wavefunctions 250
Spatiotemporal chaos 189
Spectral rigidity 245—246 272
Stability matrix 20 see
Stable manifolds 142—146
Stadium, eigenfunctions of 252—254
Stadium, eigenvalues of 243
Standard map, and Greene's method 164—167
Standard map, method of overlapping resonances for 162—163
Standard map, phase plane of 134—135
Strange attractors, basic properties of 199—202
Strange attractors, in Curry system 211
Strange attractors, in Duffing oscillator 36
Strange attractors, in Henon map 212—214
Strange attractors, in Lorenz system 208—210
Strange attractors, in Rossler system 212
Stream function 175 190
Stream lines 175
Stretching and folding 201
Subcritical bifurcation 198
Subduction 221
Superconvergent perturbation theory 107—109
Supercritical bifurcation 198
Surface of section, as a symplectic mapping 123—126 183—184
Surface of section, basic properties of 119—121
Surface of section, for chaotic advection experiment 177—181
Surface of section, for Henon — Heiles system 121—122
Surface of section, for time-dependent systems 125
Surface of section, for Toda lattice 122—123
Symplectic manifold 47
Tangent bifurcations 224
Tangent map 136—137
Tangent, bundle 47
Tangent, space 82
Tangent, vector 82
Tendrils, in Lagrangian turbulence 176 179
Tendrils, properties of 146—147
Three-body problem 89
Time-dependent integrals 6 31—33
Time-dependent integrals, of Lorenz system 346—347
Toda lattice 122—123
Tori, and definition of action variables 72
Tori, and integrable Hamiltonians 71
Tori, motion on 77—78
Tori, preservation of, under perturbation 79 106—107
Trace, of propagator 268
Transmission coefficient 294 see
Traveling wave solution, for KdV equation 284
Traveling wave solution, for mKdV equation 304
Traveling wave solution, for Sine — Gordon equation 306
Turbulence, concept of 189
Twist maps 126—128
Two-body problem 89
Two-dimensional NLS equation 317
Two-kink solution, for Sine — Gordon equation 307
Two-soliton solution, for KdV equation 299—302
Uniform approximation 233 274
Unstable manifolds 142—146
Van der Pohl oscillator 30
Variational derivative 312
Voltera equations 27
Vorticity 190 see
Wedge product 55 85
Weierstrass elliptic functions see “Elliptic functions”
Whorls, in Lagrangian turbulence 176 179
Whorls, properties of 146—147
Wigner distribution 244
Wigner function 247—248
WKB expansion 232—233
Zakharov equations 318—319
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