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| Cvitanovic P., Artuso R., Dahlqvist P. — Classical and quantum chaos |
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| Предметный указатель |
 symmetry 397
 function space 172
 , cycle weigth 150
, 79 203
3-body problem 24 513 529 599 610
3-dimensional sphere, scattering 92
3-disk, boundary orbits 392
3-disk, convergence 178 671
3-disk, cycle, analytically 95
3-disk, cycle, count 400 641
3-disk, cycle, expansion 314
3-disk, escape rate 167 303 315 319
3-disk, fractal dimension 338
3-disk, geometry 65
3-disk, hyperbolicity 137
3-disk, phase space 11 338 676
3-disk, pinball 4 65—67
3-disk, point scatterer 574
3-disk, prime cycles 16 204 261 283
3-disk, shadowing 303
3-disk, simulator 71 94 96
3-disk, symbolic dynamics 9 32 204 233
3-disk, symmetry 206 382 397 403
3-disk, transition matrix 199
Abscissa, absolute conv. 309
Abscissa, conditional conv. 309
Accelerator mode 411
action 489 500
Action, helium 532
Action, relation to period 541
Admissible periodic points 243
Admissible trajectories, number of 239
Airy function 510
Airy function at a bifurcation 510
Alphabet 198
Alternating binary tree 235
Analyticity domain 147
Anosov flows 221
Antiharmonic extension 630
ARC 203
Area, preserving map 64
Artin — Mazur zeta function 247
Attractor 36
Attractor, basin 36
Attractor, Henon 70
Attractor, strange 36 40 126
Autonomous flow 39 275
Average, space 103
Average, time 103
Averages, chaotic 363
Averaging 29
Averaging space 120
Averaging time 118
Axiom A, systems 182
Baker’s map 66
Balmer spectrum 480
Basin of attraction 36
Bernoulli polynomials 176
Bernoulli shift 175
Bi-infinite itinerary 200
Bifurcation, Airy function approximation 510
Bifurcation, bizarre 629
Bifurcation, generic 67
Bifurcation, Hopf 425
Bifurcation, saddle-node 66
Billiard, map 65
Billiards 64 66
Billiards, stability 83
Binary symbolic dynamics, collinear helium 537
Binary tree, alternating 235
Birkhoff coordinates 11
Birkhoff ergodic theorem 104
Block, finite sequence 201
Block, pruning 202
Bohr 597
Bohr helium 529 543
Bohr Uetli Schwur 608
Bohr — de Broglie picture 480
Bohr — Sommerfeld quantization 480 521 609
Boltzmann 23
Boltzmann equation 422
boredom 337 579
Borges, J.L. 579
Boundary orbits 392
Bounded operators 682
Bowen 26
Brain, rat 3 27
Branch cut 357
Branch point 357
branch point singularity 358
Burnett coefficient 416
Canonical transformations 612
Canonical, transformations 82
Cartwright, M.L. 604
Cauchy caustic 492
Cauchy criterion 77
Ceiling function 58 144 190
Center 79
Chain rule 87
Chain Rule, matrix 679
Change of coordinates 41
Chaos 5 6
Chaos, caveats 8
Chaos, skeleton of 9 11
Chaos, successes 8
Character orthonormalitity 662
Character representation 658
Characteristic function 98
Characteristic polynomial 245
Chicken heart palpitations 5
Circle map, critical 428
Coarse graining 230
Coarse-graining 98
Coding see "Symbolic dynamics"
Collinear helium 24
Collinear helium, symbolic dynamics 537
Combinatorics teaching 212
Complete N-ary dynamics 199
Complexity algorithmic 258
Confession, Kepler 600
Confession, St. Augustine 97
Conjugacy 41 43
Conjugacy, invariant 91
Conjugacy, smooth 41 53 91 697
Conjugacy, topological 213
Conservation equation 617
Conservation phase-space volume 83 618
Continuity equation 490 618
Continuity, equation 108
Contour integral 152
Contracting, flow 36 40 82
Contracting, map 132
Contracting, stability eigenvalues 89 137
Convergence, abscissa of 309
Convergence, mediocre 674
Convergence, radius 147
Convergence, super-exponential 171
Convexity 130
Coordinate, change 41 43
Coordinate, longitudinal 501
Coordinate, transformations 53
Copenhagen school x 609
Correlation, decay, power law 351
Correlation, function 186
Correlation, spectrum 187
Correlation, time 325
Cost function 279
Covering-symbolic dynamics 201
Critical point 88
Critical, point 210
| Critical, value 211 413
Cumulant, expansion 244 247 298
Cumulant, expansion, Plemelj — Smithies 686
Curvature, correction 295
Curvature, expansion 29 295
CYCLE 10
Cycle, expansion 17 295
Cycle, expansion, 3-disk 314
Cycle, expansion, finite subshift 304
Cycle, expansion, stability ordered 305
Cycle, expon 520
Cycle, fundamental 245 295
Cycle, limit 126
Cycle, point 201
Cycle, prime 138 201 261 269
Cycle, prime, 3-disk 283
Cycle, prime, Henon map 282
Cycle, pruning 251
Cycle, stability 87 283
Cycle, stable 88
Cycle, superstable 88
Cycle, unstable 11
Cycle, weigth 150
Cycles, fundamental 672
Cyclic, invariance 269
Cyclic, symmetry 242
de Broglie wavelength 484
Decay, rate 158
Degree of freedom 8
Delta function, Dirac 100 483
density 98 617
Density of states, Green’s function 483
Density of states, quantum 483
Density of states, semiclassical 517
Density, evolution 22
Desymmetrization, 3-disk 403
Determinant, Fredholm 690
Determinant, graph 257
Determinant, Hadamard 148
Determinant, spectral 21 148 243
Determinant, spectral for flows 149
Determinant, trace relation 244
Determinant, trace-class operator 683
Deterministic dynamics 5
Deterministic flow 99
Deterministic, dynamics 34
Differential equations, ordinary, almost 52
Diffraction, Green’s function 562
Diffraction, Keller 570
Diffraction, Sommerfeld 570
Diffusion, constant 122
Diffusion, partial differential equations 46
Dike map 213
Dimension, box counting 340
Dimension, fractal 339
Dimension, generalized 2
Dimension, Henon attractor 284
Dimension, information 340
Dimension, intrisic 8
Dirac delta function 100
Dirichlet series 308
Dissipative, map 132
distribution 47
Divergence rate, local 129
Doubling map 180
Duffing oscillator 38
Duffing system 50
Dynamical system, infinite 55
Dynamical system, smooth 17 18 29 255 466 469 471 604
Dynamical, system 33 34
Dynamical, system, deterministic 34
Dynamical, system, gradient 53
Dynamical, system, smooth 34
Dynamical, systems, equivalent 42
Dynamical, transitivity 240
Dynamical, zeta function 16 151
Dynamical, zeta function, Euler product rep. 151
Dynamics, deterministic 5
Dynamics, hyperbolic 205
Dynamics, irreversible 37
Dynamics, reversible 37
Dynamics, stochastic 5
Dynamics, symbolic 8 198 200 328
Dynamics, symmetry 661
Dynamics, topological 198 200 202
D’Alambert’s wave equation 46
EDGE 203
Eigendirections 74
Eigenfunction, energy 481
Eigenfunctions, Perron — Frobenius 170
Eigenstate see "Eigenfunction"
Eigenvalue, exponential spacing 149
Eigenvalue, spectral determinant 171
Eigenvalue, zero 499
Eigenvalues 158
Elliptic, partial differential equations 46
Elliptic, stability 83
Enemy, thy 352
English, plain 201
Ensemble, microcanonical 131
Entropy, barrier 311
Entropy, topological 6 240 252 257
Equation of variations 74
Equilibrium, measure see "Natural measure"
Equilibrium, point 39 80 102
Equivalence of dynamical systems 42
Ergodic average 104
Ergodic theorem, multiplicative 131
Ergodic theory 104
Escape rate 102
Escape rate, 3-disk 319
Escape, intermittency 361
Escape, rate 12 321
Escape, rate, 3-disk 303 315
Essential spectral radius 172
Essential, spectral radius 176
Euler — Maclaurin formula 187
Euler, formula 171 702
Euler, limit 81
Euler, product 155
Euler, product rep., dynamical zeta function 151
Euler, totient function 430
Evolution, group 52 696
Evolution, kernel, probabilistic 99
Evolution, operator 20 125
Evolution, operator, quantum 482
Evolution,semigroup 126
Expanding stability eigenvalues 89 137
expectation value 121 132
Exponent, stability 89
Exponential of a matrix 76
Exponential proliferation 20 258
Exponential, convergence 147 171
Extremal point 498
False zeros 155
Farey map 349 375
Farey mediant 431
Farey series 430
Farey tree 431
Feynman 597
Feynman path integral 497
Finite subshift, cycle expansion 304
First return function 58 371
Fixed point 269
Fixed point, maps 70
Fixed point, marginally stable 349
Floquet multipliers 136
Flow 34 37
Flow, autonomous 39 275
Flow, contracting 36 40 82
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