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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

: | | ID
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Involutions, calculation of Fermi mapping bifurcations      227229
Involutions, product of      169 201202
Ion cyclotron heating      650651
Islands      see also Resonance
Islands, amplitude of      114 121
Islands, magnetic      418ff
Islands, primary      51
Islands, second-order      see Second-order islands
Islands, secondary      51
Islets of stability      256 see
Itatani, R.      (87 126 270 Fukuyama
Izrailev, F.M.      113 (313 Chirikov (374 Gadiyak 374 (392 403 Chirikov 443 444 570 582 647 (653 Casati (654 Chirikov^al.)
Jacobi's identity      11
Jacobian matrix      20 203 271 459 461 509510 562563
Jaeger, F.      99 113 121 248 293 364 620 625 650
Jeffries, C      548
Jensen, M.H.      528 529 531 533 594 596 597 621 625
Johnston, S.      134
Jordan, W.      (649 Gibson
K-systems      304ff 654
Kadanoff, L.P.      172 249 620 624
KAM surface      46 61 378 see
KAM surface, curve      49
KAM surface, for Lagrangian turbulence in fluids      643
KAM theory      49 174ff
KAM theory, conditions for      174
KAM theory, converse      289ff
KAM theory, moderate nonlinearity for      182183
KAM theory, smoothness condition      180182 221222
KAM theory, sufficient irrationality for      182183
KAM theory, sufficient nonlinearity for      177180
KAM theory, tori, variational principal for      249
Kamimura, T.      348 349
Kaneko, I.      442 533 614 616 618 619
Kantz, H.      576 577 578
Kao, Y.H.      548
Kaplan and Yorke map      477
Kaplan, J.      476 557
Karimabadi, H.      240
Karney, C.F.F.      87 90 91 92 126 128 129 342 343 650
Kaufman, A.N.      87 126 127 134 268 651 653 654
KdV equation      443 448
Keeler, J.D.      613 614 615 618
Keller, J.      653
Kepler problem      34
Khinchin, A.Ya.      273
Kicked rotor      219
Kim, S.Y.      349
King, G.P.      99 601 602
Klein, A.      249
Knobloch, E.      640 641 643
Kobayashi, T.      545
Kolmogorov entropy      see KS entropy
Kolmogorov, A.N.      3 71 149 175 304 309 629
Kolomensky, A.A.      647
Kolovski, A.R.      449
Konishi, T.      442
Kopell, N.      652
Kramers, H.A.      1
Krein collision      209
Krein's theorem      209
Krilin, L.      648
Krishnaprasad, P.S.      48
Kruskal, M.D.      1 77 93 103 (141 Northrop 439 448 (457 Northrop 648
Krylov, N.      93 103 304
KS entropy      308
KS entropy, determination of      312ff
KS entropy, for Henon Heiles system      316318
KS entropy, relation to Liapunov exponents      304305
Kuckes, A.F.      650
Kulsrud, R.M.      77
Kummer, M.      645
Kuramoto, Y.      653
Lacina, J.      648
Lagrangian      7
Lagrangian, averaged, for closed orbits      155157
Lahiri, A.      541
Laing, E.W.      13 (72 110 131 Dunnett 132 (147 Dunnett
Lamb, G.      43 439
Landau model      see Transition to turbulence
Landau, L.D.      7 322 634
Landolfi, M.      445 446 447
Lanford, O.      66 67 461 466 (509 Collet
Langer, J.S.      620 625 626 627 629
Laslett, L.J.      109 647
Lattice maps      613 see
Lazar, N.      650
Leach, P.G.L.      32
Lebedev, A.N.      647
Lee, D.K.      (436 437 Carreras
Legendre transformation      9 593
Lennard Jones system      441442
Lewis, H.R.      Jr.
Li, C-T.      249 497
Liapunov exponent      298ff
Liapunov exponent, determination of      312ff
Liapunov exponent, for dissipative maps and flows      460461
Liapunov exponent, for high-dimensional systems      447 456
Liapunov exponent, for integrable systems      312313
Liapunov exponent, for logistic map      504
Liapunov exponent, for one-dimensional map      497 499
Liapunov exponent, for quadratic map      499
Liapunov exponent, for tent map      502504
Liapunov exponent, higher order      301302
Liapunov exponent, numerical calculation of      315ff
Liapunov exponent, relation between maps and flows      302
Liapunov exponent, relation to fractal dimension      376377
Liapunov exponent, relation to KS entropy      304305
Liapunov exponent, symmetry of      301
Liapunov exponent, test for stochasticity      315317
Liapunov, A.M.      298
Libchaber, A.      638
Libration      22
Lichtenberg, A.J.      14 24 58 (62 Tennyson 77 (99 Jaeger 99 113 121 194 195 196 216 221 222 224 226 237 238 248 (248 Jaeger et 254 (210 211 219 292 Howard 289 290 325 328 345 348 351 352 358 (374 379 382 383 384 386 390 392 394 Tennyson (419 421 423 Freis All (429 Gell (440 Howard (451 Goeddeef (647 650 Jaeger 641 (650 Wyeth (650 Howard 650 651
Lie transformations      133ff
Lie transformations, adiabatic invariants      141ff
Lie transformations, applied to pendulum      138140
Lie transformations, applied to pondermotive force      144147
Lie transformations, applied to slowly varying harmonic oscillator      142144
Lie transformations, comparison with mixed variables      133134
Lie transformations, elimination of secularity      141142
Lie transformations, evolution operator      135
Lie transformations, for second harmonic of standard mapping      259262
Lie transformations, general theory      135ff
Lie transformations, generating function      135
Lie transformations, Lie operator      135
Lie transformations, perturbation series      136ff
Lie transformations, resonant denominators      138
Lie transformations, second order invariants for waveparticle resonance      147148
Lie transformations, superconvergent series      152ff
Lieberman, M.A.      58 61 (62 Tennyson (99 Jaeger 99 216 (216 Lichtenberg 221 222 224 (226 Lichtenberg (248 Jaeger 248 289 290 (210 211 219 228 292 Howard (324 Lichtenberg 325 328 (344 Lichtenberg 351 352 368 385 386 (374 379 382 383 384 386 390 392 Tennyson 393 397 (404 405 Chirikov (440 Howard (451 Goedde 534 535 536 537 650 (649 Jaeger (650 WLYeth (650 Howard 575 584 585 586 587 588
Limit cycle      63 462466 461
Linear stability      196ff
Linear stability, for Fermi mapping      223225
Linear stability, for quadratic map      483485
Linear stability, for separatrix mapping      236237
Linear stability, for standard mapping      253256
Linear stability, for two dimensional mapping      202ff
Linear stability, in higher dimensions      208211
Linearized motion      195ff see
Liouville's theorem      14 459
Lipshitz cone      290
Littlejohn, R.      45 103 134
Littlewood, J.E.      144
Liu, C.S.      (141 648 Northrop
Livi, R.      445
Livingston, M.S.      (646 Courant
Lo Destro, L.L.      (650 Smith
Lo Vecchio, G.      441
Logistic map      479ff 614
Longcope, D.W.      239
Lorenz system      65ff
Lorenz system, derivation of      631633
Lorenz system, extension to many modes      633634
Lorenz system, intermittent behavior in      638
Lorenz, E.N.      6 65 66 68 69 504 631 633
Lozi, R.      474
Lundsford, G.H.      128 179 275 281
MacKay, R.S.      172 209 210 249 250 289 340 341 (342 Greene 516 532
Mackey Glass differential delay equation      see Differential delay equation
Mackey, M.C.      598
Magnetic confinement systems      418ff
Magnetic confinement systems, axisymmetric mirrors      648649
Magnetic confinement systems, diffusion in      see Diffusion in toroidal magnetic fields
Magnetic confinement systems, levitrons      361 420424
Magnetic confinement systems, nonsymmetric mirrors      99100 649 651
Magnetic confinement systems, tandem mirrors      458
Magnetic confinement systems, tokamaks      319320 423 425 430438 651
Magnetic confinement systems, toroidal      see Toroidal magnetic fields
Magnetic confinement systems, transport in      418ff
magnetic moment      88 99100 648649
Mamota, H.      (87 126 270 Fukuyama
Mandelbrot, B.      478 588
Manneville, P.      538 539 540 619 638
Mappings      162ff see
Mappings, area-preserving      52 167169
Mappings, canonical      164ff
Mappings, cat      305306
Mappings, Chirikov Taylor      see Standard mapping
Mappings, conversion to      170
Mappings, conversion to Hamiltonian form      171
Mappings, description of nonlinear      188ff
Mappings, dissipative generalized standard      510
Mappings, equivalence to Hamiltonian system      162ff
Mappings, Fermi      see Fermi acceleration
Mappings, for diffusion in magnetic fields with time variations      428431
Mappings, for diffusion of a parameter      413415
Mappings, from perturbed linear oscillators      237ff
Mappings, generalized standard      168
Mappings, how obtained      162
Mappings, integer      311
Mappings, invertible      see Invertible maps
Mappings, involution products for      see Involutions
Mappings, Kaplan and Yorke      376377
Mappings, kicked rotor      216 219
Mappings, lattice      see Spatio-temporal chaos
Mappings, linearized      195ff
Mappings, logistic      see Logistic map
Mappings, noninvertible      see Noninvertible maps
Mappings, one-dimensional      see One-dimensional noninvertible maps
Mappings, one-dimensional, for Fermi acceleration      229
Mappings, one-dimensional, for Lorenz system      69
Mappings, perturbed twist      167 200
Mappings, radial twist      168
Mappings, relation between maps and flows      302
Mappings, return      458
Mappings, reversible      202
Mappings, separatrix      see Separatrix mapping
Mappings, standard      see Standard mapping
Mappings, symplectic      208
Mappings, tent      see Tent map
Mappings, twist      see Twist mapping
Mappings, two-dimensional dissipative      see Two-dimensional dissipative maps
Mappings, two-dimensional Hamiltonian      200ff
Mappings, whisker      see Separatrix mapping
Mappings, Zaslavskii      477
Marcus, R.A.      654
Marinko, D.      (652 Hudson
Markov process      321
Marsden, J.      380
Marsden, J.E.      45 48 213
Martin, S.      534
Maschke, E.K.      634
Maselko, J.      534
Maslov index      653
Mather, J.N.      172 250 289 290
Matrix, eigenvalues and eigenvectors for      196ff
Matrix, symplectic      197200
Matthaeus, W.H.      638
Maurer, J.      638
May, R.M.      458 497
McDonald, S.W.      653 654
McLaughlin, J.B.      561
McNamara, B.      53 54 55 93 128 134 135 141 144 147 148 149 151 645
McNamara, B.S.      605 608
Mean residue      271273 276278
Mean, space and time      295 see
Meiss, J.D.      172 195 (339 Mackay 341 (342 Cary 343
Melnikov Arnold integral      233235 391
Melnikov's method      560ff
Melnikov's method, application to Duffing's equation      565567
Melnikov's method, application to mappings      568569
Melnikov, V.K.      56 186 380
Method of averaging      see Averaging method
Metropolis, N.      (443 Bivins 497
Miller, B.N.      441
Mirror symmetry for quadratic map      457 481482 490 504
Misiurewicz, M.      474
Mitropolsky, N.      1 93 103 648
Mixing      302304 308
Mixing, for baker's transformation      60
Mixing, for hard sphere gas      60 304
Mixing, for Lagrangian turbulence in fluids      643
Mixing, for logistic map      504
Mixing, for Lorenz attractor      66
Mode-locking      466 526528 534
Modulation, of phase or frequency      365369
Modulational diffusion      373 399ff 647
Modulational diffusion, multiplet layer formation      364369 400401
Modulational diffusion, thin layer, thick layer, and trapping regimes      365369
Momenta, generalized      8
Montgomery, D.      638
Month, M.      (648 Herreraet 648
Monticello, D.A.      (436 White
Montroll, E.W.      (152 154 199 201 Eminhizer
Morosov, A.D.      561
Morozov, A.I.      419
Moser, J.      3 150 163 175 181 182 183 185 222 645 646
Moses, E.      640
Motz, H.      651
Multifractals      588ff see
Multiplet      see Modulational diffusion
Murakami, S.      240
Murray, N.      336 338 339 342 (344 348 349 Lichtenberg 372
Musazzi, S.      (637 Giglio
Mutual information      599
Nag, T.      541
Nagashima, T.      315
Nauenberg, M.      495
Navier Stokes equation      65 629 634
Nayfeh, A.      134
Near-integrable systems      10 48ff
Near-integrable systems, as area-preserving mappings      167ff
Near-integrable systems, dissipative perturbation of      571ff
Near-integrable systems, Fermi acceleration      5758
Near-integrable systems, Henon and Heiles      5256
Nekhoroshev bound      398
Nekhoroshev, N.N.      62 398 438
Nekrasov, A.K.      650
Nevins, W.M.      (429 Gell 433 434 435
Newhouse, S.      553 635
Newton's method, for solving mapping equations      168
Newton's method, relocated      157
Newton's method, superconvergence of      150151
Nierwetberg, J.      497
Noise      see Extrinsic diffusion Numerical Power
noise reduction      610613
Noisy data      595
Nonautonomous Hamiltonian      see Hamiltonian nonautonomous
Noninvertible maps      65 532533 535537 see
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