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CONTENTSxvby surviving pilot courses based on this book, by providing invaluable insights,by teaching us, by inspiring us.
Page 1 and 2: . Chaos: Classical and QuantumI: De
Page 3 and 4: CONTENTSiii5.3 Stability of Poincar
Page 5 and 6: CONTENTSv18 Cycle expansions 29918.
Page 7 and 8: CONTENTSviiPart II: Quantum chaos29
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 17 and 18: CHAPTER 1. OVERTURE 2We start out b
Page 19 and 20: CHAPTER 1. OVERTURE 4Figure 1.1: A
Page 21 and 22: CHAPTER 1. OVERTURE 6In a game of p
Page 23 and 24: CHAPTER 1. OVERTURE 81.3.2 When doe
Page 25 and 26: CHAPTER 1. OVERTURE 10Figure 1.6: B
Page 27 and 28: CHAPTER 1. OVERTURE 12Figure 1.9: T
Page 29 and 30: CHAPTER 1. OVERTURE 14x(t)δ x(t) =
Page 31 and 32: CHAPTER 1. OVERTURE 16We could now
Page 33 and 34: CHAPTER 1. OVERTURE 18Figure 1.11:
Page 39 and 40: CHAPTER 1. OVERTURE 242. the set is
Page 41 and 42: CHAPTER 1. OVERTURE 26Spatiotempora
Page 43 and 44: CHAPTER 1. OVERTURE 28A guide to ex
Page 45 and 46: References 30[1.11] K.T. Alligood,
Page 47 and 48: Chapter 2Go with the flowKnowing th
Page 49 and 50: CHAPTER 2. GO WITH THE FLOW 3400000
Page 51 and 52: CHAPTER 2. GO WITH THE FLOW 36or an
Page 53 and 54: CHAPTER 2. GO WITH THE FLOW 38Figur
Page 55 and 56: CHAPTER 2. GO WITH THE FLOW 40As x
Page 57 and 58: CHAPTER 2. GO WITH THE FLOW 42Röss
Page 59 and 60: REFERENCES 44(a) For what times do
Page 61 and 62: Chapter 3Discrete time dynamicsDo i
Page 63 and 64: CHAPTER 3. DISCRETE TIME DYNAMICS 4
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CHAPTER 3. DISCRETE TIME DYNAMICS 5
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References 60References[3.1] W. S.
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CHAPTER 4. LOCAL STABILITY 62Figure
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CHAPTER 4. LOCAL STABILITY 66Solvin
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CHAPTER 4. LOCAL STABILITY 70with t
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CHAPTER 4. LOCAL STABILITY 72zFigur
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CHAPTER 4. LOCAL STABILITY 74In the
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CHAPTER 4. LOCAL STABILITY 76determ
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CHAPTER 4. LOCAL STABILITY 78follow
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CHAPTER 4. LOCAL STABILITY 80expans
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REFERENCES 824.6. A contracting bak
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CHAPTER 5. CYCLE STABILITY 84show,
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CHAPTER 5. CYCLE STABILITY 86and de
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CHAPTER 5. CYCLE STABILITY 88ith ei
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CHAPTER 5. CYCLE STABILITY 90where
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References 92[5.2] G. Floquet, “S
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CHAPTER 6. GET STRAIGHT 94field wil
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CHAPTER 6. GET STRAIGHT 96eeFigure
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CHAPTER 6. GET STRAIGHT 98energy up
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CHAPTER 6. GET STRAIGHT 100Figure 6
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CHAPTER 6. GET STRAIGHT 1026.5 Rect
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CHAPTER 6. GET STRAIGHT 104Résumé
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EXERCISES 106Exercises6.1. Coordina
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Chapter 7Hamiltonian dynamicsTruth
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CHAPTER 7. HAMILTONIAN DYNAMICS 110
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REFERENCES 118matrix is given by⎡
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Chapter 8BilliardsThe dynamics that
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CHAPTER 8. BILLIARDS 122Figure 8.3:
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CHAPTER 8. BILLIARDS 124θϕFigure
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REFERENCES 1268.1. A pinball simula
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Chapter 9World in a mirrorA detour
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CHAPTER 9. WORLD IN A MIRROR 130As
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CHAPTER 9. WORLD IN A MIRROR 132An
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CHAPTER 9. WORLD IN A MIRROR 134f(x
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CHAPTER 9. WORLD IN A MIRROR 136Fig
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CHAPTER 9. WORLD IN A MIRROR 138Fig
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CHAPTER 9. WORLD IN A MIRROR 140(a)
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CHAPTER 9. WORLD IN A MIRROR 142...
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CHAPTER 9. WORLD IN A MIRROR 1449.5
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CHAPTER 9. WORLD IN A MIRROR 146For
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EXERCISES 1481. Show that in the po
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References 150[9.8] B. Lauritzen,
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Chapter 10Qualitative dynamics, for
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CHAPTER 10. QUALITATIVE DYNAMICS, F
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REFERENCES 172How this kneading seq
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Chapter 11Qualitative dynamics, for
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EXERCISES 190Exercises11.1. A Smale
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References 192[11.9] R. Bowen and O
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References 194[11.46] P.H. Richter,
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CHAPTER 12. FIXED POINTS, AND HOW T
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REFERENCES 210p Λ p∑xp,i0 0.7151
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Chapter 13CountingThat which is cro
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CHAPTER 13. COUNTING 214the shift o
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CHAPTER 13. COUNTING 216Table 13.1:
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CHAPTER 13. COUNTING 218So the gene
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CHAPTER 13. COUNTING 220Figure 13.3
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CHAPTER 13. COUNTING 222and the top
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CHAPTER 13. COUNTING 224Table 13.2:
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CHAPTER 13. COUNTING 226Example 13.
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CHAPTER 13. COUNTING 228and t 1 app
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EXERCISES 230to other entropies.In
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EXERCISES 232Figure: (a) A unimodal
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References 234[13.6] J. Riordan, An
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CHAPTER 14. TRANSPORTING DENSITIES
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EXERCISES 250time average (14.21) i
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REFERENCES 25214.9. Invariant measu
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Chapter 15AveragingFor it, the myst
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CHAPTER 15. AVERAGING 256Figure 15.
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CHAPTER 15. AVERAGING 258vector a i
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CHAPTER 15. AVERAGING 2601f(x) 0.5F
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CHAPTER 15. AVERAGING 262As a matte
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CHAPTER 15. AVERAGING 264Figure 15.
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CHAPTER 15. AVERAGING 266As we can
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EXERCISES 268CommentaryRemark 15.1
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References 270[15.5] D. Ruelle, J.
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CHAPTER 16. TRACE FORMULAS 272weigh
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CHAPTER 16. TRACE FORMULAS 274given
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CHAPTER 16. TRACE FORMULAS 276(R. A
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CHAPTER 16. TRACE FORMULAS 278eigen
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CHAPTER 16. TRACE FORMULAS 280Figur
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REFERENCES 28216.2. General weights
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CHAPTER 17. SPECTRAL DETERMINANTS 2
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EXERCISES 296appropriate designatio
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References 298[17.2] M. Pollicott,
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CHAPTER 18. CYCLE EXPANSIONS 300whe
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CHAPTER 18. CYCLE EXPANSIONS 302Tab
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Table 18.2: 3-disk repeller escape
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CHAPTER 18. CYCLE EXPANSIONS 306Fig
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CHAPTER 18. CYCLE EXPANSIONS 308For
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CHAPTER 18. CYCLE EXPANSIONS 310The
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CHAPTER 18. CYCLE EXPANSIONS 312the
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CHAPTER 18. CYCLE EXPANSIONS 314A D
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CHAPTER 18. CYCLE EXPANSIONS 316“
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EXERCISES 318−z 4 (8 t 1213 + 4 t
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Chapter 19Discrete factorizationNo
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CHAPTER 19. DISCRETE FACTORIZATION
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EXERCISES 334was derived in ref. [1
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Chapter 20Why cycle?“Progress was
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CHAPTER 20. WHY CYCLE? 338limit γ,
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CHAPTER 20. WHY CYCLE? 340guarantee
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CHAPTER 20. WHY CYCLE? 342Now, we c
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CHAPTER 20. WHY CYCLE? 344for fancy
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REFERENCES 346References[20.1] F. C
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CHAPTER 21. WHY DOES IT WORK? 348Th
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CHAPTER 21. WHY DOES IT WORK? 35221
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CHAPTER 21. WHY DOES IT WORK? 3541f
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CHAPTER 21. WHY DOES IT WORK? 356We
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CHAPTER 21. WHY DOES IT WORK? 358di
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CHAPTER 21. WHY DOES IT WORK? 36011
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CHAPTER 21. WHY DOES IT WORK? 362sp
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CHAPTER 21. WHY DOES IT WORK? 364We
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CHAPTER 21. WHY DOES IT WORK? 366es
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EXERCISES 370Exercises21.1. What sp
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References 372[21.28] W. Tucker,
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CHAPTER 22. THERMODYNAMIC FORMALISM
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EXERCISES 382CommentaryRemark 22.1
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References 384[22.7] C. Shannon, Be
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CHAPTER 23. INTERMITTENCY 386Figure
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CHAPTER 23. INTERMITTENCY 388of the
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CHAPTER 23. INTERMITTENCY 390• f
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CHAPTER 23. INTERMITTENCY 392exactl
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CHAPTER 23. INTERMITTENCY 394Im zIm
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CHAPTER 23. INTERMITTENCY 39610 -2
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CHAPTER 23. INTERMITTENCY 398The ge
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CHAPTER 23. INTERMITTENCY 400is mea
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CHAPTER 23. INTERMITTENCY 402expans
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CHAPTER 23. INTERMITTENCY 40423.3.2
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CHAPTER 23. INTERMITTENCY 40623.4 B
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CHAPTER 23. INTERMITTENCY 408Exampl
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EXERCISES 410Exercises23.1. Integra
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References 412[23.18] D. H. Mayer,
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CHAPTER 24. DETERMINISTIC DIFFUSION
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EXERCISES 432Exercises24.1. Diffusi
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Chapter 25Turbulence?I am an old ma
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CHAPTER 25. TURBULENCE? 436Figure 2
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CHAPTER 25. TURBULENCE? 438This is
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CHAPTER 25. TURBULENCE? 440Figure 2
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CHAPTER 25. TURBULENCE? 44222Figure
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CHAPTER 25. TURBULENCE? 444From (25
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CHAPTER 25. TURBULENCE? 4460.80.70.
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CHAPTER 25. TURBULENCE? 4480.60.50.
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EXERCISES 450variational) methods t
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References 452[25.12] A. K. Kassam
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CHAPTER 26. NOISE 454Fluid dynamics
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CHAPTER 26. NOISE 45626.3 Weak nois
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CHAPTER 26. NOISE 45826.4 Weak nois
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CHAPTER 26. NOISE 460sinners (and n
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References 462[26.8] G. E. Uhlenbec
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Chapter 27Relaxation for cyclistsCy
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−1 0 1 x iCHAPTER 27. RELAXATION
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Table 27.1: All prime cycles up to
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CHAPTER 27. RELAXATION FOR CYCLISTS
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References 478[27.10] D. Pingel, P.
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CHAPTER 28. IRRATIONALLY WINDING 48
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EXERCISES 496Remark 28.9 Farey mode
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References 498[28.23] E.C. Titchmar
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Chapter 29PrologueAnyone who uses w
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CHAPTER 29. PROLOGUE 502In this app
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CHAPTER 29. PROLOGUE 504the quantum
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Chapter 30Quantum mechanics, briefl
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CHAPTER 30. QUANTUM MECHANICS, BRIE
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EXERCISES 510Exercises30.1. Dirac d
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CHAPTER 31. WKB QUANTIZATION 512Fig
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CHAPTER 31. WKB QUANTIZATION 514The
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CHAPTER 31. WKB QUANTIZATION 516Fig
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CHAPTER 31. WKB QUANTIZATION 518Air
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REFERENCES 520imation. Hint: n! =
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CHAPTER 32. SEMICLASSICAL EVOLUTION
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EXERCISES 542Exercises32.1. Dirac d
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Chapter 33Semiclassical quantizatio
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CHAPTER 33. SEMICLASSICAL QUANTIZAT
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References 556[33.11] P. Cvitanovi
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CHAPTER 34. QUANTUM SCATTERING 558s
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CHAPTER 34. QUANTUM SCATTERING 560F
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CHAPTER 34. QUANTUM SCATTERING 562s
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CHAPTER 34. QUANTUM SCATTERING 564t
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CHAPTER 34. QUANTUM SCATTERING 566H
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REFERENCES 568aRaThe full quantum m
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References 570[34.30] Following the
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CHAPTER 35. CHAOTIC MULTISCATTERING
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Chapter 36Helium atom“But,” Boh
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CHAPTER 36. HELIUM ATOM 592Figure 3
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CHAPTER 36. HELIUM ATOM 59436.2.2 S
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CHAPTER 36. HELIUM ATOM 596symmetri
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CHAPTER 36. HELIUM ATOM 598p S p /2
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CHAPTER 36. HELIUM ATOM 600The simp
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CHAPTER 36. HELIUM ATOM 602with the
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CHAPTER 36. HELIUM ATOM 6041/ζ (l)
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CHAPTER 36. HELIUM ATOM 606reveals
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EXERCISES 608energetically highest
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Chapter 37Diffraction distraction(N
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CHAPTER 37. DIFFRACTION DISTRACTION
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References 624[37.7] H. Primack et.
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References 626chaos is a rigid skel
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References 628We conclude cautiousl
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INDEX 630stable, 74superstable, 74d
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INDEX 632Lorenz flow, 42, 56, 57, 9
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INDEX 634stationary phase, 217stati
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Chaos: Classical and QuantumVolume
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APPENDIX A. A BRIEF HISTORY OF CHAO
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References 650[A.8] G.S. Ezra, K. R
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APPENDIX B. LINEAR STABILITY 652Her
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APPENDIX B. LINEAR STABILITY 654If
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APPENDIX B. LINEAR STABILITY 656M c
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APPENDIX B. LINEAR STABILITY 658Sec
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APPENDIX B. LINEAR STABILITY 660The
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Appendix CImplementing evolutionC.1
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APPENDIX C. IMPLEMENTING EVOLUTION
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APPENDIX C. IMPLEMENTING EVOLUTION
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References 668[C.3] B.A. Shadwick,
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APPENDIX D. SYMBOLIC DYNAMICS TECHN
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EXERCISES 682We find that for compl
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APPENDIX F. FINDING CYCLES 684F.1.2
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APPENDIX F. FINDING CYCLES 686highe
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APPENDIX G. TRANSPORT OF VECTOR FIE
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REFERENCES 696on an appropriate sur
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Appendix HDiscrete symmetries of dy
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APPENDIX H. DISCRETE SYMMETRIES OF
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. ..1APPENDIX H. DISCRETE SYMMETRIE
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EXERCISES 724CommentaryRemark H.1 L
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Appendix IConvergence of spectralde
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APPENDIX I. CONVERGENCE OF SPECTRAL
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APPENDIX J. INFINITE DIMENSIONAL OP
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References 746[J.9] B. Simon, Quant
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APPENDIX K. STATISTICAL MECHANICS R
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EXERCISES 768RésuméThe geometriza
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References 770[K.3] D. Ruelle. Stat
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Appendix LNoise/quantum corrections
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APPENDIX L. NOISE/QUANTUM CORRECTIO
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References 786Table L.1: Real part
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Appendix TProjectsYou are urged to
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APPENDIX T. PROJECTS 866T.1 Determi
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APPENDIX T. PROJECTS 868Describe th
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APPENDIX T. PROJECTS 870figure T.1
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References 872T.2 Deterministic dif
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References 874Attempt a numerical e
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