Contents - ChaosBook

More documents

Recommendations

Info

CONTENTSvi24 Deterministic diffusion 41324.1 Diffusion in periodic arrays .....................41424.2 Diffusion induced by chains of 1-d maps ..............41824.3 Marginal stability and anomalous diffusion .............424résumé 428 commentary 430 exercises 432 references 43225 Turbulence? 43425.1 Fluttering flame front ........................43525.2 Infinite-dimensional flows: Numerics ...............43825.3 Visualization ............................43925.4 Equilibria of equilibria .......................44025.5 Why does a flame front flutter? ...................44225.6 Periodic orbits ............................44525.7 Intrinsic parametrization ......................44525.8 Energy budget ............................446résumé 449 commentary 450 exercises 450 references 45126 Noise 45326.1 Deterministic transport .......................45326.2 Brownian diffusion .........................45526.3 Weak noise .............................45626.4 Weak noise approximation .....................458résumé 459 commentary 459 exercises 461 references 46127 Relaxation for cyclists 46427.1 Fictitious time relaxation ......................46527.2 Discrete iteration relaxation method ................47027.3 Least action method .........................474résumé 474 commentary 475 exercises 478 references 47828 Irrationally winding 48028.1 Mode locking ............................48128.2 Local theory: “Golden mean” renormalization ...........48628.3 Global theory: Thermodynamic averaging .............48828.4 Hausdorff dimension of irrational windings ............48928.5 Thermodynamics of Farey tree: Farey model ............492résumé 494 commentary 494 exercises 497 references 498
CONTENTSviiPart II: Quantum chaos29 Prologue 50129.1 Quantum pinball ..........................50229.2 Quantization of helium .......................504commentary 505 references 50630 Quantum mechanics, briefly 507exercises 51131 WKB quantization 51231.1 WKB ansatz .............................51231.2 Method of stationary phase .....................51531.3 WKB quantization .........................51631.4 Beyond the quadratic saddle point .................518résumé 519 commentary 520 exercises 520 references 52132 Semiclassical evolution 52232.1 Hamilton-Jacobi theory .......................52232.2 Semiclassical propagator ......................53032.3 Semiclassical Green’s function ...................534résumé 539 commentary 540 exercises 543 references 54433 Semiclassical quantization 54533.1 Trace formula ............................54533.2 Semiclassical spectral determinant .................55033.3 One-dof systems ..........................55233.4 Two-dof systems ..........................553résumé 554 commentary 555 exercises 556 references 55634 Quantum scattering 55834.1 Density of states ...........................55834.2 Quantum mechanical scattering matrix ...............56234.3 Krein-Friedel-Lloyd formula ....................56334.4 Wigner time delay ..........................566commentary 568 exercises 568 references 56935 Chaotic multiscattering 57235.1 Quantum mechanical scattering matrix ...............57235.2 N-scatterer spectral determinant ..................57635.3 Semiclassical 1-disk scattering ...................58035.4 From quantum cycle to semiclassical cycle .............58635.5 Heisenberg uncertainty .......................589commentary 58936 Helium atom 59136.1 Classical dynamics of collinear helium ...............59236.2 Chaos, symbolic dynamics and periodic orbits ...........59336.3 Local coordinates, fundamental matrix ...............597
Page 1 and 2: . Chaos: Classical and QuantumI: De
Page 3 and 4: CONTENTSiii5.3 Stability of Poincar
Page 5: CONTENTSv18 Cycle expansions 29918.
Page 9 and 10: CONTENTSixPart III: Appendices on C
Page 11 and 12: CONTENTSxiContributorsNo man but a
Page 13: CONTENTSxiii4.5.1 Stability of Poin
Page 16 and 17: Chapter 1OvertureIf I have seen les
Page 18 and 19: CHAPTER 1. OVERTURE 3this material,
Page 20 and 21: CHAPTER 1. OVERTURE 5231323212Figur
Page 22 and 23: CHAPTER 1. OVERTURE 7Figure 1.4: Dy
Page 24 and 25: CHAPTER 1. OVERTURE 9Figure 1.5: Ka
Page 26 and 27: CHAPTER 1. OVERTURE 11Figure 1.7: T
Page 28 and 29: CHAPTER 1. OVERTURE 13of survivors
Page 30 and 31: CHAPTER 1. OVERTURE 15where Λ i is
Page 32 and 33: CHAPTER 1. OVERTURE 171.5.3 Cycle e
Page 34 and 35: CHAPTER 1. OVERTURE 191.6 Evolution
Page 36 and 37: CHAPTER 1. OVERTURE 21The beauty of
Page 38 and 39: CHAPTER 1. OVERTURE 23So, no proofs
Page 40 and 41: CHAPTER 1. OVERTURE 25But the power
Page 42 and 43: CHAPTER 1. OVERTURE 27measures of
Page 44 and 45: EXERCISES 29Exercises1.1. 3-disk sy
Page 46 and 47: References 31[1.29] D. Ruelle, “F
Page 48 and 49: CHAPTER 2. GO WITH THE FLOW 33Figur
Page 50 and 51: CHAPTER 2. GO WITH THE FLOW 35very
Page 52 and 53: CHAPTER 2. GO WITH THE FLOW 37asymp
Page 54 and 55: CHAPTER 2. GO WITH THE FLOW 39Z(t)3
Page 56 and 57:
CHAPTER 2. GO WITH THE FLOW 41some
Page 58 and 59:
EXERCISES 43The exercises that you
Page 60 and 61:
References 45[2.7] D. Rothman, Nonl
Page 62 and 63:
CHAPTER 3. DISCRETE TIME DYNAMICS 4
Page 64 and 65:
Page 66 and 67:
Page 68 and 69:
Page 70 and 71:
Page 72 and 73:
Page 74 and 75:
EXERCISES 59Exercises3.1. Poincaré
Page 76 and 77:
Chapter 4Local stability(R. Mainier
Page 78 and 79:
CHAPTER 4. LOCAL STABILITY 63x(t)δ
Page 80 and 81:
CHAPTER 4. LOCAL STABILITY 65Hence
Page 82 and 83:
CHAPTER 4. LOCAL STABILITY 67Exampl
Page 84 and 85:
CHAPTER 4. LOCAL STABILITY 69are fl
Page 86 and 87:
CHAPTER 4. LOCAL STABILITY 714.3 St
Page 88 and 89:
CHAPTER 4. LOCAL STABILITY 73Figure
Page 90 and 91:
CHAPTER 4. LOCAL STABILITY 75task a
Page 92 and 93:
CHAPTER 4. LOCAL STABILITY 77hand s
Page 94 and 95:
CHAPTER 4. LOCAL STABILITY 79Figure
Page 96 and 97:
EXERCISES 81The nomenclature tends
Page 98 and 99:
Chapter 5Cycle stabilityTopological
Page 100 and 101:
CHAPTER 5. CYCLE STABILITY 85Figure
Page 102 and 103:
CHAPTER 5. CYCLE STABILITY 87Exampl
Page 104 and 105:
CHAPTER 5. CYCLE STABILITY 89so a p
Page 106 and 107:
EXERCISES 91infinite set of metric
Page 108 and 109:
Chapter 6Get straightWe owe it to a
Page 110 and 111:
CHAPTER 6. GET STRAIGHT 95smoothly,
Page 112 and 113:
CHAPTER 6. GET STRAIGHT 97Figure 6.
Page 114 and 115:
CHAPTER 6. GET STRAIGHT 99Example 6
Page 116 and 117:
CHAPTER 6. GET STRAIGHT 1016.4 Rect
Page 118 and 119:
CHAPTER 6. GET STRAIGHT 1036.6 Cycl
Page 120 and 121:
CHAPTER 6. GET STRAIGHT 105Remark 6
Page 122 and 123:
References 107[6.10] I. Percival an
Page 124 and 125:
CHAPTER 7. HAMILTONIAN DYNAMICS 109
Page 126 and 127:
Page 128 and 129:
Page 130 and 131:
Page 132 and 133:
EXERCISES 117Put your right hand on
Page 134 and 135:
References 119[7.5] D.G. Sterling,
Page 136 and 137:
CHAPTER 8. BILLIARDS 121Figure 8.1:
Page 138 and 139:
CHAPTER 8. BILLIARDS 123Consider a
Page 140 and 141:
EXERCISES 125CommentaryRemark 8.1 B
Page 142 and 143:
References 127[8.7] G. Vattay, A. W
Page 144 and 145:
CHAPTER 9. WORLD IN A MIRROR 1299.1
Page 146 and 147:
CHAPTER 9. WORLD IN A MIRROR 1319.1
Page 148 and 149:
CHAPTER 9. WORLD IN A MIRROR 133{0}
Page 150 and 151:
CHAPTER 9. WORLD IN A MIRROR 135Fig
Page 152 and 153:
Page 154 and 155:
Page 156 and 157:
CHAPTER 9. WORLD IN A MIRROR 141the
Page 158 and 159:
CHAPTER 9. WORLD IN A MIRROR 143Exa
Page 160 and 161:
CHAPTER 9. WORLD IN A MIRROR 145(1)
Page 162 and 163:
EXERCISES 147Exercises9.1. 3-disk f
Page 164 and 165:
REFERENCES 1499.9. Proto-Lorenz sys
Page 166 and 167:
References 151[9.28] R. Miranda and
Page 168 and 169:
CHAPTER 10. QUALITATIVE DYNAMICS, F
Page 170 and 171:
Page 172 and 173:
Page 174 and 175:
Page 176 and 177:
Page 178 and 179:
Page 180 and 181:
Page 182 and 183:
Page 184 and 185:
Page 186 and 187:
EXERCISES 171Remark 10.2 Counting p
Page 188 and 189:
References 173[10.10] A. Boyarski,
Page 190 and 191:
Page 192 and 193:
Page 194 and 195:
Page 196 and 197:
Page 198 and 199:
Page 200 and 201:
Page 202 and 203:
Page 204 and 205:
Page 206 and 207:
REFERENCES 191(a) (easy) Consider a
Page 208 and 209:
References 193[11.26] K.T. Hansen,
Page 210 and 211:
Chapter 12Fixed points, and how to
Page 212 and 213:
CHAPTER 12. FIXED POINTS, AND HOW T
Page 214 and 215:
Page 216 and 217:
Page 218 and 219:
Page 220 and 221:
Page 222 and 223:
Page 224 and 225:
EXERCISES 209Exercises12.1. Cycles
Page 226 and 227:
References 211[12.11] B. Doyon and
Page 228 and 229:
CHAPTER 13. COUNTING 2133e n ln 2
Page 230 and 231:
CHAPTER 13. COUNTING 21513.2 Topolo
Page 232 and 233:
CHAPTER 13. COUNTING 217We could no
Page 234 and 235:
CHAPTER 13. COUNTING 219Figure 13.1
Page 236 and 237:
CHAPTER 13. COUNTING 221terms of cy
Page 238 and 239:
CHAPTER 13. COUNTING 223Example 13.
Page 240 and 241:
Table 13.3: List of the 3-disk prim
Page 242 and 243:
CHAPTER 13. COUNTING 227Figure 13.4
Page 244 and 245:
CHAPTER 13. COUNTING 229step in der
Page 246 and 247:
EXERCISES 231the corresponding tran
Page 248 and 249:
REFERENCES 233As the rule does not
Page 250 and 251:
Chapter 14Transporting densitiesPau
Page 252 and 253:
CHAPTER 14. TRANSPORTING DENSITIES
Page 254 and 255:
Page 256 and 257:
Page 258 and 259:
Page 260 and 261:
Page 262 and 263:
Page 264 and 265:
Page 266 and 267:
EXERCISES 251quence of Gaussians∫
Page 268 and 269:
References 253[14.13] G. Froyland,
Page 270 and 271:
CHAPTER 15. AVERAGING 25515.1.1 Tim
Page 272 and 273:
CHAPTER 15. AVERAGING 257of the dyn
Page 274 and 275:
CHAPTER 15. AVERAGING 259so if we c
Page 276 and 277:
CHAPTER 15. AVERAGING 261Figure 15.
Page 278 and 279:
CHAPTER 15. AVERAGING 263δx0x(0)δ
Page 280 and 281:
CHAPTER 15. AVERAGING 265Figure 15.
Page 282 and 283:
CHAPTER 15. AVERAGING 267Here we ha
Page 284 and 285:
REFERENCES 26915.1. How unstable is
Page 286 and 287:
Chapter 16Trace formulasThe trace f
Page 288 and 289:
CHAPTER 16. TRACE FORMULAS 273magni
Page 290 and 291:
CHAPTER 16. TRACE FORMULAS 275This
Page 292 and 293:
CHAPTER 16. TRACE FORMULAS 277be th
Page 294 and 295:
CHAPTER 16. TRACE FORMULAS 279the f
Page 296 and 297:
EXERCISES 281Now that we have a tra
Page 298 and 299:
Chapter 17Spectral determinants“I
Page 300 and 301:
CHAPTER 17. SPECTRAL DETERMINANTS 2
Page 302 and 303:
Page 304 and 305:
Page 306 and 307:
Page 308 and 309:
Page 310 and 311:
Page 312 and 313:
REFERENCES 297(d) Let p be all prim
Page 314 and 315:
Chapter 18Cycle expansionsRecycle..
Page 316 and 317:
CHAPTER 18. CYCLE EXPANSIONS 301We
Page 318 and 319:
CHAPTER 18. CYCLE EXPANSIONS 303For
Page 320 and 321:
CHAPTER 18. CYCLE EXPANSIONS 305Giv
Page 322 and 323:
CHAPTER 18. CYCLE EXPANSIONS 307and
Page 324 and 325:
CHAPTER 18. CYCLE EXPANSIONS 30918.
Page 326 and 327:
CHAPTER 18. CYCLE EXPANSIONS 311whi
Page 328 and 329:
CHAPTER 18. CYCLE EXPANSIONS 313Fig
Page 330 and 331:
CHAPTER 18. CYCLE EXPANSIONS 315fea
Page 332 and 333:
EXERCISES 317Exercises18.1. Cycle e
Page 334 and 335:
REFERENCES 31918.12. Ulam map is co
Page 336 and 337:
CHAPTER 19. DISCRETE FACTORIZATION
Page 338 and 339:
Page 340 and 341:
Page 342 and 343:
Page 344 and 345:
Page 346 and 347:
Page 348 and 349:
Page 350 and 351:
REFERENCES 335tonian∑H(ɛ) = −J
Page 352 and 353:
CHAPTER 20. WHY CYCLE? 337get thinn
Page 354 and 355:
CHAPTER 20. WHY CYCLE? 339of the it
Page 356 and 357:
CHAPTER 20. WHY CYCLE? 341As is usu
Page 358 and 359:
CHAPTER 20. WHY CYCLE? 3431. due to
Page 360 and 361:
EXERCISES 345connected due to the n
Page 362 and 363:
Chapter 21Why does it work?Bloch:
Page 364 and 365:
CHAPTER 21. WHY DOES IT WORK? 349in
Page 366 and 367:
CHAPTER 21. WHY DOES IT WORK? 351is
Page 368 and 369:
CHAPTER 21. WHY DOES IT WORK? 353fi
Page 370 and 371:
CHAPTER 21. WHY DOES IT WORK? 355wo
Page 372 and 373:
CHAPTER 21. WHY DOES IT WORK? 357Th
Page 374 and 375:
CHAPTER 21. WHY DOES IT WORK? 359As
Page 376 and 377:
CHAPTER 21. WHY DOES IT WORK? 3611.
Page 378 and 379:
CHAPTER 21. WHY DOES IT WORK? 363Fi
Page 380 and 381:
CHAPTER 21. WHY DOES IT WORK? 365Ex
Page 382 and 383:
CHAPTER 21. WHY DOES IT WORK? 367R
Page 384 and 385:
CHAPTER 21. WHY DOES IT WORK? 369we
Page 386 and 387:
References 371[21.7] D. Ruelle, “
Page 388 and 389:
Chapter 22Thermodynamic formalismBe
Page 390 and 391:
CHAPTER 22. THERMODYNAMIC FORMALISM
Page 392 and 393:
Page 394 and 395:
Page 396 and 397:
Page 398 and 399:
REFERENCES 383tory. Biham and Kvale
Page 400 and 401:
Chapter 23IntermittencySometimes Th
Page 402 and 403:
CHAPTER 23. INTERMITTENCY 38710.8f(
Page 404 and 405:
CHAPTER 23. INTERMITTENCY 3891a0.8F
Page 406 and 407:
CHAPTER 23. INTERMITTENCY 391It may
Page 408 and 409:
CHAPTER 23. INTERMITTENCY 393to arb
Page 410 and 411:
CHAPTER 23. INTERMITTENCY 395where
Page 412 and 413:
CHAPTER 23. INTERMITTENCY 397assumi
Page 414 and 415:
CHAPTER 23. INTERMITTENCY 399Figure
Page 416 and 417:
CHAPTER 23. INTERMITTENCY 401Table
Page 418 and 419:
CHAPTER 23. INTERMITTENCY 403for al
Page 420 and 421:
CHAPTER 23. INTERMITTENCY 405Changi
Page 422 and 423:
CHAPTER 23. INTERMITTENCY 407∫1/
Page 424 and 425:
CHAPTER 23. INTERMITTENCY 409with i
Page 426 and 427:
REFERENCES 411This leads to the fol
Page 428 and 429:
Chapter 24Deterministic diffusionTh
Page 430 and 431:
CHAPTER 24. DETERMINISTIC DIFFUSION
Page 432 and 433:
Page 434 and 435:
Page 436 and 437:
Page 438 and 439:
Page 440 and 441:
Page 442 and 443:
Page 444 and 445:
Page 446 and 447:
Page 448 and 449:
References 433[24.7] P. Cvitanović
Page 450 and 451:
CHAPTER 25. TURBULENCE? 43525.1 Flu
Page 452 and 453:
CHAPTER 25. TURBULENCE? 4372vt, t),
Page 454 and 455:
CHAPTER 25. TURBULENCE? 439Figure 2
Page 456 and 457:
CHAPTER 25. TURBULENCE? 441The equi
Page 458 and 459:
CHAPTER 25. TURBULENCE? 44310Figure
Page 460 and 461:
CHAPTER 25. TURBULENCE? 445Table 25
Page 462 and 463:
CHAPTER 25. TURBULENCE? 447The mean
Page 464 and 465:
CHAPTER 25. TURBULENCE? 449(u x ) 2
Page 466 and 467:
REFERENCES 451for finite dimensiona
Page 468 and 469:
Chapter 26NoiseHe who establishes h
Page 470 and 471:
CHAPTER 26. NOISE 45526.2 Brownian
Page 472 and 473:
CHAPTER 26. NOISE 457The left hand
Page 474 and 475:
CHAPTER 26. NOISE 459in time t is g
Page 476 and 477:
EXERCISES 461Exercises26.1. Who ord
Page 478 and 479:
References 463[26.32] O. Cepas and
Page 480 and 481:
CHAPTER 27. RELAXATION FOR CYCLISTS
Page 482 and 483:
Page 484 and 485:
Page 486 and 487:
Page 488 and 489:
Table 27.3: All prime cycles up to
Page 490 and 491:
Page 492 and 493:
EXERCISES 477Exercises27.1. Evaluat
Page 494 and 495:
Chapter 28Irrationally windingI don
Page 496 and 497:
CHAPTER 28. IRRATIONALLY WINDING 48
Page 498 and 499:
Page 500 and 501:
Page 502 and 503:
Page 504 and 505:
Page 506 and 507:
Page 508 and 509:
Page 510 and 511:
Page 512 and 513:
REFERENCES 497References[28.1] P. C
Page 514 and 515:
Chaos: Classical and QuantumVolume
Page 516 and 517:
CHAPTER 29. PROLOGUE 50129.1 Quantu
Page 518 and 519:
CHAPTER 29. PROLOGUE 5031086r 24Fig
Page 520 and 521:
REFERENCES 505References[29.1] M. B
Page 522 and 523:
CHAPTER 30. QUANTUM MECHANICS, BRIE
Page 524 and 525:
CHAPTER 30. QUANTUM MECHANICS, BRIE
Page 526 and 527:
Chapter 31WKB quantizationThe wave
Page 528 and 529:
CHAPTER 31. WKB QUANTIZATION 513Fig
Page 530 and 531:
CHAPTER 31. WKB QUANTIZATION 51531.
Page 532 and 533:
CHAPTER 31. WKB QUANTIZATION 517Fig
Page 534 and 535:
EXERCISES 519soft potential. The co
Page 536 and 537:
Chapter 32Semiclassical evolutionWi
Page 538 and 539:
CHAPTER 32. SEMICLASSICAL EVOLUTION
Page 540 and 541:
Page 542 and 543:
Page 544 and 545:
Page 546 and 547:
Page 548 and 549:
Page 550 and 551:
Page 552 and 553:
Page 554 and 555:
Page 556 and 557:
Page 558 and 559:
REFERENCES 543References[32.1] A. E
Page 560 and 561:
CHAPTER 33. SEMICLASSICAL QUANTIZAT
Page 562 and 563:
Page 564 and 565:
Page 566 and 567:
Page 568 and 569:
Page 570 and 571:
EXERCISES 555Exercises33.1. Monodro
Page 572 and 573:
Chapter 34Quantum scatteringScatter
Page 574 and 575:
CHAPTER 34. QUANTUM SCATTERING 559F
Page 576 and 577:
CHAPTER 34. QUANTUM SCATTERING 561T
Page 578 and 579:
CHAPTER 34. QUANTUM SCATTERING 563t
Page 580 and 581:
CHAPTER 34. QUANTUM SCATTERING 565W
Page 582 and 583:
EXERCISES 567CommentaryRemark 34.1
Page 584 and 585:
References 569[34.13] J.S. Faulkner
Page 586 and 587:
Chapter 35Chaotic multiscattering(A
Page 588 and 589:
CHAPTER 35. CHAOTIC MULTISCATTERING
Page 590 and 591:
Page 592 and 593:
Page 594 and 595:
Page 596 and 597:
Page 598 and 599:
Page 600 and 601:
Page 602 and 603:
Page 604 and 605:
Page 606 and 607:
CHAPTER 36. HELIUM ATOM 591eeFigure
Page 608 and 609:
CHAPTER 36. HELIUM ATOM 593765r2432
Page 610 and 611:
CHAPTER 36. HELIUM ATOM 59561010014
Page 612 and 613:
CHAPTER 36. HELIUM ATOM 597with H Q
Page 614 and 615:
CHAPTER 36. HELIUM ATOM 599S p = 2T
Page 616 and 617:
CHAPTER 36. HELIUM ATOM 6010-0.5N=5
Page 618 and 619:
CHAPTER 36. HELIUM ATOM 603and m p
Page 620 and 621:
CHAPTER 36. HELIUM ATOM 605N n j =
Page 622 and 623:
CHAPTER 36. HELIUM ATOM 607Remark 3
Page 624 and 625:
REFERENCES 609displacements along t
Page 626 and 627:
CHAPTER 37. DIFFRACTION DISTRACTION
Page 628 and 629:
Page 630 and 631:
Page 632 and 633:
Page 634 and 635:
Page 636 and 637:
Page 638 and 639:
EXERCISES 623Exercises37.1. Station
Page 640 and 641:
EpilogueNowadays, whatever the trut
Page 642 and 643:
References 627of “structural stab
Page 644 and 645:
Indexaction, 232admissibletrajector
Page 646 and 647:
INDEX 631matrix, 54, 124Gatto Nerop
Page 648 and 649:
INDEX 633Poincaré section, 41-42,
Page 650 and 651:
INDEX 635unimodal, 140winding numbe
Page 652 and 653:
Appendix AA brief history of chaosL
Page 654 and 655:
APPENDIX A. A BRIEF HISTORY OF CHAO
Page 656 and 657:
Page 658 and 659:
Page 660 and 661:
Page 662 and 663:
Page 664 and 665:
REFERENCES 6493. Hénon case: The f
Page 666 and 667:
Appendix BLinear stabilityMopping u
Page 668 and 669:
APPENDIX B. LINEAR STABILITY 653(a)
Page 670 and 671:
APPENDIX B. LINEAR STABILITY 655Usi
Page 672 and 673:
APPENDIX B. LINEAR STABILITY 657Deg
Page 674 and 675:
APPENDIX B. LINEAR STABILITY 659i.e
Page 676 and 677:
EXERCISES 661ExercisesB.1. Real rep
Page 678 and 679:
APPENDIX C. IMPLEMENTING EVOLUTION
Page 680 and 681:
APPENDIX C. IMPLEMENTING EVOLUTION
Page 682 and 683:
EXERCISES 667Note that the billiard
Page 684 and 685:
Appendix DSymbolic dynamics techniq
Page 686 and 687:
APPENDIX D. SYMBOLIC DYNAMICS TECHN
Page 688 and 689:
Page 690 and 691:
Page 692 and 693:
Page 694 and 695:
Page 696 and 697:
Appendix ECounting itinerariesE.1 C
Page 698 and 699:
Appendix FFinding cycles(C. Chandre
Page 700 and 701:
APPENDIX F. FINDING CYCLES 6852.521
Page 702 and 703:
Appendix GTransport of vector field
Page 704 and 705:
APPENDIX G. TRANSPORT OF VECTOR FIE
Page 706 and 707:
Page 708 and 709:
Page 710 and 711:
EXERCISES 695for the zeta-functionF
Page 712 and 713:
References 697[G.17] M.J. Feigenbau
Page 714 and 715:
APPENDIX H. DISCRETE SYMMETRIES OF
Page 716 and 717:
Page 718 and 719:
Page 720 and 721:
λ 3 − λ 2λ 3 − λ 2. ..⎞
Page 722 and 723:
Page 724 and 725:
Page 726 and 727:
Page 728 and 729:
Page 730 and 731:
Page 732 and 733:
Page 734 and 735:
Page 736 and 737:
Page 738 and 739:
Page 740 and 741:
REFERENCES 725The point of the abov
Page 742 and 743:
APPENDIX I. CONVERGENCE OF SPECTRAL
Page 744 and 745:
Page 746 and 747:
Page 748 and 749:
Appendix JInfinite dimensional oper
Page 750 and 751:
APPENDIX J. INFINITE DIMENSIONAL OP
Page 752 and 753:
Page 754 and 755:
Page 756 and 757:
Page 758 and 759:
Page 760 and 761:
EXERCISES 745such that the spectral
Page 762 and 763:
Appendix KStatistical mechanics rec
Page 764 and 765:
APPENDIX K. STATISTICAL MECHANICS R
Page 766 and 767:
Page 768 and 769:
Page 770 and 771:
Page 772 and 773:
Page 774 and 775:
Page 776 and 777:
Page 778 and 779:
Page 780 and 781:
Page 782 and 783:
f fff fff fff fffffffffff fff fff f
Page 784 and 785:
REFERENCES 769space H) such that fo
Page 786 and 787:
References 771[K.20] M. E. Fisher.
Page 788 and 789:
APPENDIX L. NOISE/QUANTUM CORRECTIO
Page 790 and 791:
Page 792 and 793:
Page 794 and 795:
Page 796 and 797:
Page 798 and 799:
Page 800 and 801:
REFERENCES 785Figure L.2: A typical
Page 802 and 803:
References 787[L.16] A. Wirzba, CHA
Page 804 and 805:
APPENDIX T. PROJECTS 8655. or evalu
Page 806 and 807:
APPENDIX T. PROJECTS 867Figure T.1:
Page 808 and 809:
APPENDIX T. PROJECTS 869Figure T.2:
Page 810 and 811:
REFERENCES 871for larger Λ more po
Page 812 and 813:
References 873figure 24.4 Λ D414(a
show all

Contents - ChaosBook

You also want an ePaper? Increase the reach of your titles

Delete template?

Save as template?