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Lichtenberg A.J., Liebermen M.A. Regular and Chaotic Dynamics
Lichtenberg A.J., Liebermen M.A.  Regular and Chaotic Dynamics









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: Regular and Chaotic Dynamics

: Lichtenberg A.J., Liebermen M.A.

:

This book treats nonlinear dynamics in both Hamiltonian and dissipative systems. The emphasis is on the mechanics for generating chaotic motion, methods of calculating the transitions from regular to chaotic motion, and the dynamical and statistical properties of the dynamics when it is chaotic. The book is intended as a self consistent treatment of the subject at the graduate level and as a reference for scientists already working in the field. It emphasizes both methods of calculation and results. It is accessible to physicists and engineers without training in modern mathematics. The new edition brings the subject matter in a rapidly expanding field up to date, and has greatly expanded the treatment of dissipative dynamics to include most important subjects. It can be used as a graduate text for a two semester course covering both Hamiltonian and dissipative dynamics.


: en

: /

:

ed2k: ed2k stats

: second edition

: 1992

: 692

: 18.08.2008

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Sink      63 461468 570ff see
Sitnikov, K.      645
Skew-symmetric product      199
Slater, J.C.      647
Smale, S.      185 560 645
Small denominators      see Resonant denominators
Smith, G.R.      27 87 126 127 265 269 650
Snyder, H.S.      32 224 (646 Courant 647
Solitons      see Integrable systems solition
Solomonoff, R.J.      309
Solov'ev, L.S.      419 420 427
Space average      see Mean space
Sparpaglioni, M.      (445 Livi
Spatio-temporal chaos      613ff
Spatio-temporal chaos, domain formation      614
Spatio-temporal chaos, intermittancy      617619
Spatio-temporal chaos, lattice maps      613 620
Spatio-temporal chaos, natural spatial wavelength      617
Spectrum      see Power spectrum
Sprott, J.C.      650
Stability      195ff
Stability, formal      212
Stability, linear      198200 208212
Stability, nonlinear (Liapunov)      213
Stability, spectral      see linear
Stadium problem      654
Standard mapping      168 250ff
Standard mapping, accelerator modes      253
Standard mapping, barrier transition      256
Standard mapping, bifurcations      254256
Standard mapping, conversion from Fermi to      251
Standard mapping, conversion from separatrix to      251
Standard mapping, corrections to quasilinear diffusion for      334338
Standard mapping, dissipative      519 573574
Standard mapping, effect of noise on      353ff
Standard mapping, fractal diagram for      279281
Standard mapping, Greene's method applied to      271ff
Standard mapping, Hamiltonian form      256258
Standard mapping, higher order diffusion in      328ff
Standard mapping, higher period fixed points      254256
Standard mapping, Liapunov exponent for      314
Standard mapping, overlap criterion for      258ff
Standard mapping, period 1 fixed points      253
Standard mapping, quantized      654
Standard mapping, summary of transition to global stochasticity for      291292
Stark, J.      (341 342 Greene
Stationary point      see Fixed point
Stavans, J.      636
Stein, M.L.      (497 Metropolis
Stein, P.R.      (497 Metropolis
Steinberg, V.      640
Steinman, J.      (635 637 Gollub
Stern, D.      93 141 144
Stix, T.H.      27 423
Stochastic barrier      see Barrier transition
Stochastic layer      see Resonance layer
Stochastic motion      293ff see Diffusion
Stochastic pump model      387ff
Stochastic pump model, diffusion calculation      387ff 396397
Stochastic pump model, for modulational diffusion      401405
Stochastic web      237239
Stochasticity      see also Stochastic motion
Stochasticity, across a resonance layer      62
Stochasticity, along a resonance layer      61
Stochasticity, concepts of      63 302ff
Stochasticity, extrinsic      see Extrinsic diffusion
Stochasticity, global (or strong or connected)      51 246 291292
Stochasticity, local (or weak or isolated)      246 291292
Stochasticity, parameter for standard mapping      169 250
Stochasticity, regions of      5152
Stochasticity, transition to global      245ff
Stoddard, S.D.      (38 Ford 441
Strange attractors      63ff 457ff 521ff 652 see Roessler Henon Lozi Fermi Dissipative
Strange attractors, calculation of invariant distributions for      580ff
Strange attractors, geometric properties of      474ff
Strange attractors, leaved structure of      471 586588
Strange attractors, Roux attractor      600601
Strange attractors, topology of      469471
Stream function for fluids      640643
Strelcyn, J.M.      (245 298 301 305 311 315 316 317 319 320 Benettin
Strong focusing      647
Structural stability      305
Stupakov, G.Z.      649
Sudan, R.N.      239
Sun, B.Z.      45 48 210 213
Superadiabaticity      650 651
Superconvergence      see Perturbation theory Lie KAM
Superstate orbits      492 531
Surface of section      1720
Surface of section, for billiards problem      382385
Surface of section, for dissipative systems      458
Surface of section, for driven pendulum      232
Surface, energy      see Energy surface
Surface, KAM      see KAM surface
Swift, J.      507 508
Swinney, H.L.      449 534 599 601 635
Symmetries      see Integrals isolating
Symon, K.R.      32 219 647
Symplectic integration      172
Symplectic maps      208
Symplectic maps, in many dimensions      442 451
Symplectic matrix      197200
System, decomposable      295 305
System, dissipative      see Dissipative systems
System, ergodic      see Ergodic systems
System, integrable      see Integrable systems
System, near-integrable      see Near-integrable systems
System, quantum      653654
System, reaction-diffusion      652
Szebehely, V.      646
Szepfalusy, P.      576
Tabor, M.      43 250
Takens, F.      6 182 498 (499 Newhouse 598 599 635
Tang, C      628
Tangent map      208
Tangent vector, in phase space      298
Taylor, J.B.      (72 Dunnett (99 Hastie (110 128 Dunnett 131 132 (147 Dunnett 220 (247 419 423 Rosenbluth (648 Hastie
Tayursky, V.A.      (313 Chirikov
Tel, T.      576
Teller, E.      648
Tennyson, J.I.      62 179 364 365 368 374 376 377 378 382 383 384 385 386 390 392 394 406 407 409 410 411 412 647
Tent map      502504
Thomae, S.      504 506
Three resonance theory for Arnold diffusion      see Stochastic pump model
Three-body problem      1 644645
Tiling      237 239
Time average      see Mean time
Time-dependent Hamiltonian      see Hamiltonian nonautonomous
Time-independent Hamiltonian      see Hamiltonian autonomous
Timofeev, A.V.      364 650
Toda lattice      3639
Toda, M.      36
Tomita, K.      652
Topology, change of      72
Toroidal magnetic fields      418ff
Toroidal magnetic fields, configurations      418419
Toroidal magnetic fields, diffusion in      see Diffusion in toroidal magnetic fields
Toroidal magnetic fields, drift islands in      427
Toroidal magnetic fields, drift surfaces      425
Toroidal magnetic fields, Hamiltonian form      421422
Toroidal magnetic fields, magnetic islands      418ff
Toroidal magnetic fields, magnetic surfaces      420422
Torus, in phase space      164165 375
Torus, translations on      see Twist mapping
Trajectories, exponential divergence of      298 307
Trajectories, mean exponential rate of divergence      299
Trajectories, of the Henon mapping      191192
Trajectories, on a phase space torus      164165
Trajectories, regular      20 4951
Trajectories, stochastic      5152
Trajnin, L.Ya.      (649 Ponomarenko
Transformation theory      7ff
Transformation, area preserving      see Area preserving
Transformation, canonical      see Canonical transformation
Transformation, Lie      see Lie transformation
Transient chaos      570ff
Transient chaos, chaotic repeller      536
Transient chaos, chaotic semiattractor      576
Transient chaos, Fokker Planck equation for      572
Transient chaos, in digital phase-locked loop      572
Transient chaos, in dissipative Fermi map      574576
Transient chaos, in generalized Henon map      572
Transient chaos, in quadratic map      570 576 579
Transient chaos, in standard map      573574
Transient chaos, in weakly dissipative twist maps      571
Transient chaos, local description      576580
Transient chaos, near a crisis      579ff
Transient chaos, weak dissipation      571576
Transition to turbulence      634ff
Transition to turbulence, intermittent model      638
Transition to turbulence, Landau model      634635
Transition to turbulence, period-doubling model      636637
Transition to turbulence, Ruelle and Takens model      635636
Tresser, C      532
Treve, Y.      66 446 458 474 634
Tsang, K.      574 575 584 585 586 587 588 590 592
Tsuda, I.      652
Turbulence, chemical      651653
Turbulence, fluid      634ff
Turbulence, Lagrangian      640
Turbulence, transition to      see Transition to turbulence
Turner, J.S.      (38 Ford
Turnstile      345
Twist mapping      166 296297
Twist mapping, Liapunov exponent of      313
Twist mapping, transient chaos in      571
Two-dimensional dissipative maps      508ff
Two-dimensional dissipative maps, period-doubling bifurcations in      508ff
Two-dimensional dissipative maps, quadratic      see Two-dimensional dissipative quadratic map
Two-dimensional dissipative quadratic map, expansion of general map      509510
Two-dimensional dissipative quadratic map, renormalization of      510512
Two-dimensional dissipative quadratic map, standard form      510
Two-Thirds Rule      250 287 291292
Tyson, J.J.      652
Ueda, Y.      565
Ugodnikov, A.D.      (374 Izrailev
Uhlenbeck, G.E.      293 321
Ulam, S.      2 216 443 504
Umberger, D.K.      528
Usikov, D.A.      (237 Zaslavskii
Valkering, T.P.      (219 van
Valz-Gris, F.      (653 Casati
van der Weele, J.P.      219
VanZeyts, J.B.J.      490 515
Variational Principle      8
Variational theory, for closed orbits      155156
Variational theory, for KAM tori      249
Vidal, C.      (638 Roux 652
Vivaldi, F.      (42 Bountis (62 398 404 Chirikov
von Neumann, J.      504 645
VonZeipel, H.      1 75 79 454
Vulpiani, A.      (445 Livi
Waddell, B.V.      (436 White
Walker, G.H.      247 645
Walker, J.      652
Wang, M.C.      283 321
Watari, T.      651
Watenabe, T.      651
Waters, J.      444
Watson, C.J.H.      651
Wave-particle interaction, accidental degeneracy for oblique propagation      122123
Wave-particle interaction, canonical perturbation theory for      87ff
Wave-particle interaction, global removal of resonances      131133
Wave-particle interaction, Hamiltonian      87
Wave-particle interaction, intrinsic degeneracy for perpendicular propagation      124
Wave-particle interaction, level curves (invariant curves)      9093
Wave-particle interaction, numerical results      126129
Wave-particle interaction, resonances      8990
Wave-particle interaction, resonant      122ff
Wave-particle interaction, second-order islands for      268
Wedge operator      301 564
Wegmann, K.      652
Weinstein, A.      (48 213 Holm
Weiss, J.B.      640 641 643
Wentzel, G.      1
Westervelt, R.M.      594
White, R.B.      328 (328 Rechester 334 335 (346 Karney 353 (304 354 Rechester 354 436
Whiteman, K.J.      53 54 55 93 141 144 645
Whittaker, E.T.      7 14 16 24 39 141 645
Widom, M.      576
Wiedemann, H.      648
Winding number      526 530
Winfree, A.      652
Wintner, A.      646
WKB solution      76
Wolf, A.      507 508 602 603
Wong, B.W.      519 520 522
Wood, B.P.      237 238 242 248 358 361 363 442
Wright, H.L.      441
Wronskian determinant      30
Wyeth, N.C.      650
Yamada, T.      651
Yamazaki, H.      651
Yasnetsky, A.N.      (649 Ponomarenko
Yeh, W.L.      548
Yorke, J.      476 497 549 550560 571 576 579 580 590 591 597
Yoshida, H.      43
Yurchenko, V.I.      (649 Ponomarenko
Zabusky, N.J.      439 448
Zaiken, A.N.      652
Zakharov, M.Yu.      (237 Zaslavskii
Zaslavskii map      477
Zaslavskii, G.M.      216 237 (247 Rosenbluth 298 (419 423 Rosenbluth {All Filonenko 519 653 654
Zhabotinsky, A.M.      652
Zisook, A.B.      506 507
Zubarev, D.N.      93 103
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