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| Lichtenberg A.J., Liebermen M.A. — Regular and Chaotic Dynamics |
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| Ïðåäìåòíûé óêàçàòåëü |
Noninvertible maps, chaotic behavior in 497ff
Nonlinearity parameter, definition 114
Northrop, T.G. 141 648
Noyes, R.M. 652
Numerical errors 310—312
Numerical errors, in finding KAM curve 275
O'Neil, M.N. 439 448 449
Olsen, L.F. (652 Degn
One-dimensional noninvertible maps 478ff
One-dimensional noninvertible maps, for Roessler attr actor 469
One-dimensional noninvertible maps, logistic see “Logistic map”
One-dimensional noninvertible maps, quadratic see “One-dimensional quadratic map”
One-dimensional quadratic map 479ff
One-dimensional quadratic map, bifurcation phenomena 482—485
One-dimensional quadratic map, fixed points and stability 481—485
One-dimensional quadratic map, intermittent behavior in 538ff 638
One-dimensional quadratic map, invariant distributions for 498—502
One-dimensional quadratic map, Liapunov exponent for 497—499
One-dimensional quadratic map, mirror symmetry in 481—482
One-dimensional quadratic map, periodic cycles for 495—497
One-dimensional quadratic map, power spectrum for 493—495 504—508
One-dimensional quadratic map, renormalization procedures 485—493
One-dimensional quadratic map, reverse bifurcations of chaotic bands 504
One-dimensional quadratic map, trajectories for 484—485
One-dimensional quadratic map, transient chaos in 576 579
Oono, Y. (653 Yamazaki
Orthogonal metrics 418
Orzag, S.A. 630
Oscillation center diffusion see “Resonance streaming”
Oscillator, harmonic see “Harmonic oscillator”
Oscillator, harmonic, multidimensional 374ff 437ff
Oscillator, harmonic, nonlinear 73
Oseledec, V.I. 298 300 301 498
Oster, G.F. 497
Ott, E. 341 342 458 474 547 550—560 571 576 579 580 582 590 591 597 654
Overlap criterion 247 258ff 291
Overlap criterion, comparison with Fermi acceleration 264
Overlap criterion, for first and second harmonies 259—262
Overlap criterion, for many degrees of freedom 440
Overlap criterion, for multiplet 364—369 400
Overlap criterion, including separatrix layer thickness 262—264
Overlap criterion, simple 259
Packard, N. (68 Farmer 478 598
Papayannopoulos, T. 646
Parker, T.S. 458
Particle-wave interaction see “Waveparticle interaction”
Pasta, J.R. 2 443 (443 Bivins
Pecelli, G. (645 Churchill
Peierls, R.F. (648 Herrera
Pendulum, driven one-dimensional 231ff
Pendulum, driven, second-order islands for 265ff 268ff
Pendulum, exact solution for 27—29
Pendulum, mean half-period for separatrix motion 392—393
Pendulum, phase or frequency modulated 364—368
Pendulum, second order solution by Lie transformations 138—140
Pendulum, solution by perturbation theory 81—83
Penrose 0. 293
Percival, I.C. 172 250 339 341 654
Pereira, N. (134 Kaufman 268 269
Perez, R. 532 548
Period-doubling bifurcations 65 see “Reverse
Period-doubling bifurcations, in Henon attractor 472—474
Period-doubling bifurcations, in one-dimensional quadratic map 482ff
Period-doubling bifurcations, in Roessler attractor 468—471
Period-doubling bifurcations, in two-dimensional dissipative maps 508ff
Period-doubling bifurcations, model for transition to turbulence see “Transition to turbulence”
Periodic delta function 171
Periodic delta function, use in billiards problem 387
Periodic delta function, use in Fermi acceleration 229
Periodic delta function, use in standard mapping 256
Periodic orbits see also “Fixed points”
Periodic orbits, in one-dimensional quadratic map 482ff
Periodic orbits, series solutions for 154ff 195
Perran, J.W. (652 Degn
Perrini, U. (637 Giglio
Perturbation theory, adiabatic 93ff
Perturbation theory, applied to periodic orbits of the Henon and Heiles system 158—161
Perturbation theory, canonical 70ff
Perturbation theory, canonical adiabatic 96ff
Perturbation theory, contrasting slow and small 95—96
Perturbation theory, for Fermi acceleration 229—230
Perturbation theory, for periodic orbits 154ff
Perturbation theory, higher order 72 see
Perturbation theory, Newton's method 150—151
Perturbation theory, one degree of freedom 78ff
Perturbation theory, pendulum 81—83
Perturbation theory, power series expansion 72—74
Perturbation theory, secular 72 109ff
Perturbation theory, small denominators 75—78
Perturbation theory, super convergent 71
Perturbation theory, superconvergent methods 149ff
Perturbation theory, two or more degrees of freedom 83ff
Perturbation theory, using Lie transformations see “Lie transformations”
Perturbation theory, variational method 155—156
Perturbation theory, with explicit time dependence 85—87
Pesin, Ya.B. 298 304
Pettini, M. 445 446 447
Phase space, boundary 13
Phase space, coarse graining 85 303 647 652
Phase space, contraction 459—460
Phase space, extended 15—16
Phase space, for dissipative system 459—460
Phase space, in Lorenz system 66
Phase space, incompressible flow in 14
Phase space, motion 12ff
Phase space, reduced 16 19
Phase space, tangent vector in 264
Phase space, tiling 238
Phase space, trajectory 12
Phase space, transformation of 171
Phase space, volume 13
Phase space, volume contraction of 459—460
Phase space, web 239
Plateau diffusion see “Diffusion plateau”
Poincare surface of section see “Surface of section”
Poincare — Bendixson theorem 460
Poincare — Birkhoff theorem 183—185
Poincare, H. 1 14 71 75 79 93 185 645
Poisson brackets 10—11
Poisson brackets, use with Lie transformations 135
Pomeau, Y. 538 539 540 548 638
Pomphrey, N. 250
Ponderomotive force 144—147 460
Ponomarenko, V.G. 649
Post, H.W. (202 Roberts (219 van
Power spectrum 634
Power spectrum, for fluid velocity 636
Power spectrum, for heat transport 636
Power spectrum, for Lorenz system 67
Power spectrum, for one-dimensional quadratic map 493—495 504—508
Power spectrum, for Roessler attractor 469—470
Prediction, short and long time see “Reconstruction”
probability density see also “Invariant distribution”
Probability density, conditional 329
Probability density, transition 321
Procaccia, L. 478 533 538 545 546 547 589 591 592 603 604 606
Prodi, G. 634
Pustylnikov, L.D. 219
Quadratic form, invariance of 199
Quadratic mappings, De Vogelaere 514
Quadratic mappings, Hamiltonian 512ff
Quadratic mappings, Henon's dissipative see “Henon attractor”
Quadratic mappings, Henon's twist 191ff
Quadratic mappings, logistic see “Logistic map”
Quadratic mappings, one-dimensional noninvertible see “One-dimensional quadratic map”
Quadratic mappings, two-dimensional dissipative see “Two-dimensional dissipative map”
Quantum systems 653—654
Quasiaccelerator mode 345ff
Quasicrystal 239
Quasilinear diffusion 329 414
| Quasilinear diffusion, corrections to 334—335
Quasimode 444
Quispel, G.R.W. 202
Rabinovich, M.I. (373 Izrailev 458
Ram, A.K. 364
Ramani, A. (42 Ablowitz
Rand, D. 531
Random phase assumption 323—324 388
Random sequences 309—310
Randomness 309ff
Randomness, definition of 309
Randomness, relation to complexity 309—310
Rannou, P. 311
Ratin, T. 45 48 213
Rayleigh numbers 632
Rayleigh — Benard convection 65 630 631—634
Rayleigh — Benard convection, in binary fluids 640
Reaction-diffusion systems 613
Rechester, A.B. 27 328 334 335 (346 Karney 353 355 423
Reconstruction 597ff
Reconstruction, autocorrelation function for 599
Reconstruction, delay coordinates for 598ff
Reconstruction, embedding dimension for 589ff
Reconstruction, forecasting 606
Reconstruction, global 608ff
Reconstruction, local 604ff
Reconstruction, mutual information for 599
Reconstruction, noise reduction 61 Off
Reconstruction, of fractal dimension 602ff
Reconstruction, redundancy for 600
Reconstruction, singular systems analysis for 601
Reconstruction, statistical quantities 602ff
Reduction 44ff
Redundancy 600
Renormalization 485ff 542ff
Renormalization group 491 542ff
Renormalization, for intermittancy 542ff
Renormalization, for one-dimensional quadratic map 485ff
Renormalization, for power spectra 493—495 504—508
Renormalization, for resonance islands 122
Renormalization, for two resonances 249 281ff 291—292
Renormalization, for two-dimensional dissipative quadratic map 509—512
Renormalization, for two-dimensional Hamiltonian map 512—519
Renormalization, functional 491—493 542ff
Renormalization, transformation 286
Renyi, A. 589
Repeller, chaotic 576
Rescaling parameters see “Renormalization”
Residue see “Mean residue”
Resonance layer 51 61—62 375—380 383—384 406—407
Resonance streaming 406ff see
Resonance streaming, diffusion calculation 407—412
Resonance streaming, geometric construction 406—407
Resonance streaming, numerical results 410—412
Resonance streaming, of oscillation center 406—407 414—416
Resonance streaming, relation to diffusion of a parameter 416—418
Resonance surface see “Resonance layer”
Resonance vector 374—380 406—407
Resonance, between unperturbed frequencies 111
Resonance, coupling 385—386 393ff 409—410
Resonance, effect of 77—78
Resonance, global removal of 128ff
Resonance, higher order 117ff
Resonance, in multidimensional oscillations 373ff
Resonance, islands 49 70
Resonance, overlap see “Overlap criterion”
Resonance, passage through 101
Resonance, primary 51
Resonance, removal of 11 Off
Resonance, removal of secondary 119—120
Resonance, secondary 51 109
Resonance, secondary in wave-particle interaction 124—126
Resonant denominators 85 98
Reverse bifurcations, in one-dimensional quadratic map 505
Reverse bifurcations, in Roessler attractor 469—470
Reversibility 202
Reynold's number 629
Rigid body 46—48 214
Roberts, J.A.G. 202
Rod, D.L. (641 Churchhill
Roessler attractor 466—471
Roessler, O.E. 468 652
Rognlien, T.D. 650
Rosenbluth, M.N. 247 (328 353 354 355 Rechester 419 423 425 (436 White 649 650
Rossi, A. (634 Roux (652 Vidal
Rotation 22
Roundoff errors 310—312
Roux, J.C. 600 634 638 (652 Vidal
Rowlands, G. (94 Cohen 406 412 413 416 581 (648 Cohen 649
Rubinow, S. 653
Rudnick, J. 495 498 538 543
Ruelle and Takens model see “Transition to turbulence”
Ruelle, D. 6 458 598 635 (635 Newhouse 652
Ruffo, S. (445 Uwi
Russell, D.A. 476 477
Ruytov, D.D. 649
Sagdeev, R.Z. (237 Zarlavskii (423 Filonenko 429 435 (247 428 435 Rosenbluth
Saltzman, B. 633
Samec, T.K. 650
Sandpiles see “Self-organized criticality”
Saramito, B. 634
Satija, I.I. 531
Sato, T. 240 373 381 (651 Watari
Scaling index spectrum 592ff
Scheidecker, J.-P. 298 315 440
Schluter, A. 94 648
Schmidt, G. 256 259 279 280 425 519 520 522 (523 Chen
Schmits, R.A. 652
Schroedinger equation, nonlinear 449
Schuster, H.G. 458 491 538 541 542 543 545 546 547
Second-order islands 189 194 248 264ff 291
Second-order islands, for wave-particle interaction 268
Second-order islands, near elliptic fixed points 265ff
Second-order islands, near the separatrix 268ff
Segur, H. (42 Ablowitz 42 (42 Bounds 43
Seidl, M. 109 650
Self-organized criticality 620ff
Self-organized criticality, avalanches 621
Self-organized criticality, coupled differential equations 625ff
Self-organized criticality, coupled mappings 620ff
Self-organized criticality, earthquake model 625—628
Self-organized criticality, sandpiles 620
Self-organized criticality, scaling spectra for 622—625
Separatrix crossings 363ff
Separatrix layer see “Resonance layer”
Separatrix mapping 236ff 243
Separatrix mapping, conversion to standard mapping 251
Separatrix mapping, use in overlap criterion 262—264
Separatrix, for pendulum 28
Separatrix, motion for driven pendulum 231ff
Separatrix, motion for Duffing's equation 565—567
Separatrix, stochastic motion near 51 560ff
Separatrix, web 237—239
Sessler, A. 219 647
Shadowing theorem see “Noise reduction”
Shafranov, V.D. 420 427
Shaw, R. 64 (68 Farmer 458 468 469 (478 Packard 497 499 500 501 502 582
Shenker, S.J. 249 530
Shepelyanski, D.L. 342 (392 397 403 654 Chirikov 654
Shimada, I. 315
Shraiman, B.I. 531
Siambis, J. 649
Sidorowich, J J. 605 607 610 611
Siegel, C.L. 181 645 646
Simo, C 473 474
Simo, C. 213
Sinai, Ya.G. 60 67 304 342
Sine — Gordon equation 450
Singular systems analysis for reconstruction 601
Singularity see “Fixed point”
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