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| Lichtenberg A.J., Liebermen M.A. — Regular and Chaotic Dynamics |
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 see “Scaling index spectrum”
Aamodt, R.E. 364 650
Abarbanel, H.D.I. 328 607
Ablowitz, M.J. 42
Accelerator modes, effect on diffusion 344 345—349
Accelerator modes, for standard mapping 253
action 171—172
Action integral, relation to integral invariant 16—17
Action space 375—380
Action space, for billiards problem 381—383
Action space, for resonance streaming 410 417
Action, change in resonance crossing 369—372
Action, change, for driven pendulum 233—234
Action-angle variables 21 ff
Action-angle variables, for central force 35
Action-angle variables, for coupling resonance 395—396
Action-angle variables, for harmonic oscillator 23
Action-angle variables, for pendulum 27 82
Action-angle variables, for two resonances 282—283
Adiabatic barrier see “Barrier transition”
Adiabatic invariant 16 24 71 93ff
Adiabatic invariant, by canonical methods 93ff
Adiabatic invariant, by noncanonical methods 102ff
Adiabatic invariant, from Lie transformations 141ff
Adiabatic invariant, of harmonic oscillator see “Harmonic oscillator”
Ahlers, G. 635
Alexeev, M.V. 645
Alfven, H. 4 648
Angelopoulos, V. 240
Anosov, D.V. 305 610
Anosov-systems see “C-systems”
Antonsen, T.M., Jr. (654 Ott
Area-preserving transformation, condition for perturbed twist map 203
Area-preserving transformation, definition 19
Arnold diffusion 60—62 238 373 401 646 647 649
Arnold diffusion, calculation of 386ff
Arnold diffusion, examples of 380ff
Arnold diffusion, for coupling resonance 393ff
Arnold diffusion, for many resonances 397ff
Arnold tongue 528
Arnold web 61 379—383
Arnold, V.I. 3 5 14 59 60 61 66 163 175 185 188 197 198 302 306 307 373 380 528
Asteroid belt 646
Asymptotic expansions see “Expansions asymptotic”
Attractors, basin boundaries 51ff 558ff
Attractors, basins of 461
Attractors, crises see “Crises”
Attractors, definition of 461 ff
Attractors, semiattractor 576—578
Attractors, simple see “Fixed point” “Sink” “Limit
Attractors, strange see “Strange attractors”
Autocorrelation 342
Autocorrelation, for reconstruction 599
Autonomous Hamiltonian see “Hamiltonian autonomous”
Avalanches see “Self-organized critically”
Averaging, applied to harmonic oscillator 106—109
Averaging, Kruskal's method 103—106
Averaging, method of 71
Averaging, multiple time scale 103
Averaging, over slower of fast phases 111
Avez, A. 59 163 185 188 302 306 307
Bachelert, S. (652 Vidal
Bak, P. 527 528 530 532 534 620 621 623 624 625 628
Baker's transformation 303 607
Bardet, R. 650
Barrier transition 246
Barrier transition, for electron cyclotron heating 650
Barrier transition, for Fermi acceleration 225
Barrier transition, for separatrix mapping 237
Barrier transition, for standard mapping 256
Barrier transition, for two resonances 287—288
Barrier transition, summary of criteria for 291 ff
Basin of attraction see “Attractors”
Baxter, D.C. 650
Beam-beam interaction 647
Behringer, R.P. 635
Belousov — Zabotinsky reaction 652—653
Belykh, V.N. 534
Ben-Misrachi, A. 538 545
Benettin, G. 245 298 299 301 305 311 315 316 317 319 438 445
Bensimon, D. 172 594
Benson, S.V. (635 636 Gollub
Berge, P. 547
Berk, H.L. 651
Berman, C.P. 449
Berman, G.P. 654
Berman, R.H. 255
Bernoulli shifts 307—309
Bernstein, G.M. 534 535 536 537 572 573
Bernstein, I.B. 650
Berry, M.V. 150 185 193 293 303 653 654
Bers, A. 87 126 (364 Ram
Berz, M. 173
Bhattacharee, A. (342 Cary
Bialek, J. 256 279 280
Bifurcation theory for Hamiltonian maps 508ff
Bifurcations 461 ff
Bifurcations, exchange of stability 463—464 484
Bifurcations, for one-dimensional quadratic map 482—485
Bifurcations, for two-dimensional dissipative quadratic map 510—512
Bifurcations, for two-dimensional Hamiltonian map 512ff
Bifurcations, Hopf 463—464 465 541 634—635
Bifurcations, of Fermi mapping 226—229
Bifurcations, of standard mapping 254—256
Bifurcations, period-doubling 209 463 see
Bifurcations, pitchfork 463—464 484ff 511 540
Bifurcations, reverse see “Reverse bifurcations”
Bifurcations, tangent (saddle-node) 209 462 464 496 538
Bifurcations, transcritical 463
Billiards problem 381ff
Billiards problem, coupling resonance 385—386 393—397
Billiards problem, thick layers 382 387—389
Billiards problem, thin layers 382 389—393
Birkhoff, G.D. 2 93 185 290 645
Bivins, R.L. 439 443 449
Bochelart, S. (638 Roux
Boghosian, B.M. 45
Bogoliubov, N.N. 1 93 103 648
Boozer, A. 422
Born, M. 2 72 81 134 653
Bounds, T.C. 42 154 158 159 160 201 273 513
Bowen, R. 610
Brahic, A. 216
Brambilla, M. 427
Bridges, R. 581
Brillouin, L. 224
Brock, W.A. 598
Broomhead, P.S. 599 601 602
Broucke, R. 209 210
Bruhwiler, D.L. 364 370 371 372
Bruns, H. 645
Bunimovich, L.A. 67 342
Byers, J.A. 650 (650 Smith
C-systems 305—307
Canonical perturbation see “Perturbation theory canonical”
Canonical transformation, general theory 7ff
Canonical transformation, to rotating coordinates 111
Canonical variables 8
Cantor set 63 374—375 588
Cantor set, two-scale 588—589 593—594
Cantorus 195 328
Capacity see “Fractal dimension”
Capel, H.W. (202 Roberts (219 van
Carlson, J.M. 620 625 626 627 629
Carreras, B. 436 437 438
Cary, J.R. 43 134 (134 Kaufman 136 151 152 342 364 369 370 371 372 425 651
Casartelli, M. (311 Benettin
Casati, G. 312 506 644 653 654
Casimir 45ff 213—215
Caustics 653
| Central force 33—36
Chaiken, J. 640
Chaitin, GJ. 309
Chandrasekhar, S. 293 408 648
Chao, A.W. 210
Characteristic exponents see “Liapunov exponents”
Characteristic function 343
Chate, H. 619
Chen, C 523 524 525
Chernikov, A.A. 217
Chhabra, A. 597
Chillingworth, D.R.J. 561
Chirikov, B.V. 4 29 57 62 99 109 114 151 163 169 182 183 216 219 234 236 242 244 247 253 254 256 258 264 298 (312 Casati 313 315 334 364 369 (373 Gadiyak 374 385 392 393 395 397 398 399 403 404 405 406 412 413 418 437 438 443 444 570 644 646 647 648 649 (653 Casati
Chua, L.O. 458
Churchill, R.C. 645
Circle map 525ff
Coarse-graining 89 647 653
Cohen, R.H. 94 (216 226 254 328 Lichtenberg 406 412 413 416 648 649
Collet, P. 458 485 504 505 509 514
complexity 309
Conditionally periodic motion 22
Conditionally periodic motion, for central force 33
Conjugate variables 8
Constant of the motion 11
Continued fractions 273—274 286
Contopoulos, G 179 326 645 646
Contraction of phase space volume 459—466
Converse KAM theorem 289—291
Coordinates, delay 598ff
Coordinates, generalized 8
Coordinates, noncanonical 44ff
Coordinates, rotating 109ff
Correlation dimension see “Fractal dimension”
Correlation function, for quadratic map 506—507
Correlations 342ff 506
Courant, E.D. 32 224 646 647
Crawford, J, D. 328 462 466 468
Cremers, J. 608 610
Crises 523 548ff
Crises, boundary crisis 551ff
Crises, exterior crisis 550
Crises, hysteresis 555
Crises, in one-dimensional maps 549—551
Crises, interior crisis 550 553
Crises, transient chaos near 579ff
Crutchfield, J. (68 Farmer 469 470 (478 Packard 557 605 608 614 619 638
Curry, J.H. 473 633 635
Dangelmayr, G. 640
Darboux's theorem 45
de Vogeleare, R. 172 201
Decomposable system 295 305
Degeneracy, accidental 113—114 119 122—123 178
Degeneracy, intrinsic 113—117 178—179
Degeneracy, intrinsic, for Kepler problem 36
Degeneracy, transition from accidental to intrinsic 124—125
Degn, H. 652
Delay coordinates 578ff
Deprit, A. 2 134 136 645
Devil's staircase 526
Dewar, R.L. 134 136
Differential delay equation, Mackey — Glass 598 603—606
Differential equations, Floquet form for 31
Differential equations, for dissipative flows 458
Differential equations, linear 29ff
Differential equations, with periodic coefficients 30—32
Diffusion see also “Fokker — Planck equation”
Diffusion coefficient 322
Diffusion coefficient, relation to friction coefficient 322
Diffusion for many degrees of freedom 437ff
Diffusion for many degrees of freedom, Fermi — Pasta — Ulam system 440
Diffusion for many degrees of freedom, for attracting sheets 440—441
Diffusion for many degrees of freedom, for Lennard — Jones potential 441—442
Diffusion in toroidal magnetic fields 412 418ff
Diffusion in toroidal magnetic fields, magnetic islands 422—425
Diffusion in toroidal magnetic fields, magnetic surfaces 420—422
Diffusion in toroidal magnetic fields, mapping for 428ff
Diffusion in toroidal magnetic fields, numerical results 433—435
Diffusion in toroidal magnetic fields, static fields 425ff
Diffusion in toroidal magnetic fields, tearing and disruptions in tokamaks 436—438
Diffusion in toroidal magnetic fields, time varying fields 428ff
Diffusion of a parameter 413ff
Diffusion of a parameter, for oscillation center 414—416
Diffusion of a parameter, in toroidal magnetic field 428ff
Diffusion of a parameter, mapping for 413—415
Diffusion of a parameter, relation to resonance streaming 416—418
Diffusion tensor 408—411
Diffusion, across resonance layers 386—387
Diffusion, along resonance layers 373 386 399ff see
Diffusion, Arnold see “Arnold diffusion”
Diffusion, banana 412 427—428 434
Diffusion, coupling resonance 393ff
Diffusion, extrinsic see “Extrinsic diffusion”
Diffusion, Fourier path technique 329ff
Diffusion, higher order 329ff
Diffusion, in action space 320ff
Diffusion, in billiards problem see “Billiards problem”
Diffusion, many resonance 397ff
Diffusion, modulational see “Modulational diffusion”
Diffusion, neoclassical 428
Diffusion, oscillation center see “Resonance streaming”
Diffusion, Pfirsch — Schliiter 428
Diffusion, plateau 427—428 433—435
Diffusion, pseudo-classical 433
Diffusion, quasilinear see “Quasilinear diffusion”
Diffusion, self-consistent problem 436ff
Digital phase-locked loop, circle map representation 534—537
Digital phase-locked loop, transient chaos in 572
DIMENSION see “Fractal dimension”
Dipole, axisymmetric magnetic 648
Dissipative systems 62ff 570ff
Dissipative systems, resonance streaming in 412
Dorizzi, B. 43
Doveil, F. 249 274 281 284 286 287 289
Dragt, A.J. 134 168 186 187 648 649
Driscoll, C.F. 439 448 449
Dubois, M. 548
Duffing's equation 565—567
Duffing's equation, chaotic motion in 567
Dunnett, D.A. 72 110 128 147
Earthquake model 625—628
Ecke, R.E. 528 529
Eckmann, J.-P. 458 485 504 509 513 514 598 635 (635 Collet
Edmonds, P.H. 650
Eigenvalues 196ff
Eigenvalues, for Liapunov exponents 300
Eigenvalues, for two-dimensional mappings 200ff
Eigenvalues, of cat mapping 306—307
Eigenvalues, symmetry of 197—199
Eigenvectors 196ff
Eigenvectors, for Liapunov exponents 300
Eigenvectors, for two-dimensional mappings 200ff
Eigenvectors, of cat mapping 306—307
Einstein, A. 101
Eldridge, O. 650
Electron cyclotron resonance heating 650—651
Elliptic orbits, for two-dimensional mapping 205—206
Elliptic points see “Fixed point elliptic”
Eminhizer, C.R. 152 154 195 201
Energy surface 61 376—380 406—407
Energy—Casimir method 213—215
entropy 308—309 446 609 see
Equipartition of energy 445—447 452—453
Equipartition of energy, relaxation time 447
Ergodic systems 59—60 295ff 308
Ergodic systems, baker's transformation 59—60
Ergodic systems, hard sphere gas 59—60
Ergodic systems, Lorenz attractor 65ff
Errors, numerical see “Numerical errors”
Errors, roundoff see “Roundoff errors”
Escande, D.F. 250 274 279 281 284 286 287 289 (371 Cary
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