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Hilborn R.C. Ч Chaos and nonlinear dynamics
Hilborn R.C. Ч Chaos and nonlinear dynamics

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Ќазвание: Chaos and nonlinear dynamics

јвтор: Hilborn R.C.


This is the only book that introduces the full range of activity in the rapidly growing field of nonlinear dynamics to an audience of students, scientists, and engineers with no in-depth experience in the area. The text uses a step-by-step explanation of dynamics and geometry in state space as a foundation for understanding nonlinear dynamics. It goes on to provide a thorough treatment of such key topics as differential equation models and iterated map models (including a derivation of the famous Feigenbaum numbers), the surprising role of number theory in dynamics, and an introduction to Hamiltonian dynamics. This is the only book written at this introductory level to include the increasingly important field of pattern formation, along with a survey of the controversial questions of quantum chaos. Important analytical tools, such as Lyapunov exponents, Kolmogorov entropies, and fractal dimensions, are treated in detail. With over 200 figures and diagrams, and both analytic and computer exercises following every chapter, the book is ideally suited for use as a text or for self-instruction. An extensive collection of annotated references brings the reader into contact with the literature in nonlinear dynamics, which the reader will be prepared to tackle after completing the book.

язык: en

–убрика: ‘изика/Ќелинейна€ динамика, ’аос/

—татус предметного указател€: √отов указатель с номерами страниц

ed2k: ed2k stats

»здание: 2nd edition

√од издани€: 2000

 оличество страниц: 650

ƒобавлена в каталог: 10.09.2005

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ѕредметный указатель
$f(\alpha)$ spectrum      393Ч404
$g(\Lambda)$      404Ч412
1/f noise      256 479
action      280Ч285 491 505Ч506
Action-angle variables      280Ч289
algorithmic complexity      508Ч510
Antimonotonicity      197
Area preserving maps      303Ч309
Arnold cat map      308Ч309 499
Arnold diffusion      294
Arnold tongues      225 231 372
Asymptotically stable      164
Attracting set      see "Attractor(s)"
Attractor(s)      22 32 67 78Ч79
Attractor(s), chaotic, defined      172
Attractor(s), strange, defined      342
Autocorrelation function      383Ч384
Autocorrelation time      383Ч388
Autonomous system      76
Average Lyapunov exponent      172 324 419
Averaging method      592Ч596
Baker's transformation      208
Band merging      194
Bare winding number      221
Basin boundaries      79 352Ч353
Basin of attraction      22 32 79 107
Benard      See "Rayleigh Ч Benard"
Bernoulli shift      190Ч192
Bifurcation      166Ч171
Bifurcation diagram      11 15Ч18 24Ч25 107Ч108
Bifurcation diagram, diode circuit      17Ч18
Bifurcation diagram, Gaussian map      194Ч196
Bifurcation diagram, Henon map      200
Bifurcation diagram, logistic map      24Ч25 48 58 59 180 263
Bifurcation diagram, sine-circle map      237Ч238
Bifurcation theory      106Ч113 541Ч546
Bifurcation, defined      11Ч12
Bifurcation, global      122 541 545
Bifurcation, Hopf      111Ч113 137
Bifurcation, local      121Ч122
Bifurcation, pitchfork      see "Period-doubling"
Bifurcation, point      106Ч113
Bifurcation, saddle-node      109
Bifurcation, tangent      109 254Ч256 259
Billiards      311
Biological models and noise      243Ч244
Birkhoff series      281
Bouncing ball model      517
Boundary crisis      260Ч262
Bounded system      85
Boussinesq approximation      550
Box-Counting Dimension      342Ч344 390
Brusselator model      100 109Ч110
Butterfly effect      38
Canonical transformation      280Ч282
Cantor set      344Ч345
Cantor set, asymmetric and weighted      398Ч402
Capacity dimension      see "Boxcounting dimension"
Cardiac cells      241Ч242
Cat map      308Ч309
Cellular automata      445Ч448
Center (fixed point)      see "Elliptic point"
Center manifold      543
Chaos      3Ч9
Chaos, criteria for      150 172
Chaos, definition      6Ч7
Chaotic attractor      120
Chaotic bands      25 179Ч182
Chaotic scattering      479
Chaotic transients      67 118 122 145
Characteristic direction      88 91 99
Characteristic equation      93 97Ч98
Characteristic exponent      105Ч106
Characteristic multiplier      105 113 132
Characteristic value      80Ч81 84 94 99
Chemical reactions      91
Chirikov standard map      304Ч307
Circle map      219Ч227
Cluster of initial conditions      86Ч87 96 150Ч152 159Ч160
Codimension      541
Coexistence of regular and chaotic motion      289Ч292 299Ч303
Coherent structures      435
Commensurate frequencies      211
Comparison time      384
Complex eigenvalues      94Ч96
complexity      39 434Ч435 490
Composition rule      169 573
Computer networks      514Ч515
Computer programs      64Ч66 560Ч567
Computers and chaos      61Ч63
Conservative system      272Ч273
Constant energy surface      276
Continued fractions      231Ч234
Continuity equation      452
Control parameter      11 15 30
Controlling chaos      515Ч516
Convection      see "Lorenz model"
Convergent      232
Correlation dimensions      see "Dimensions correlation"
Correlation integral      355
Correlation sum      355 (see also "Generalized correlation sum")
Correspondence principle      493
Coupled modes      465
Coupled oscillator models      442Ч445
Crisis      122 138 260Ч268
Crisis-induced intermittency      265
Critical point      173
Critical state      478
criticality      240
Cycles      see "Limit cycles"
Damping      see "Dissipation"
Darcy's law      475
Degrees of freedom      72Ч74 274 276
Delay-differential equation      490
Dendrites      473
Determinant      98Ч100
Determinism      3 6 37Ч39
Deterministic chaos      6
Devil's staircase      227
Diffusion      450Ч456
Diffusion-limited aggregation      471Ч474
Dimensions, box-counting      342 390
Dimensions, correlation      354Ч368 392Ч394
Dimensions, fractal      341Ч354
Dimensions, generalized      389 390 392Ч394
Dimensions, Hausdorff      354 383
Dimensions, information      392 409
Dimensions, Lyapunov      383
Dimensions, pointwise      359
Dimensions, similarity      348Ч352
Dimensions, topological      354
Diode circuit      8Ч17 51Ч52 160Ч161 510Ч511
dispersion relation      465
Dissipation      see also "Dissipative systems"
Dissipation and Jacobian      97Ч99
Dissipation and sum of Lyapunov exponents      148Ч152
Dissipative standard map      309Ч311
Dissipative systems      78Ч79 86Ч87
Divergence of nearby trajectories      13Ч14 16 25 37Ч39 172
Divergence theorem and dissipation      87 96Ч97
Double crisis      267
Doubling transformation      574
Drift ring      214 227
Duffing oscillator      71 579Ч583
Dynamical localization      507
Dynamical partition function      416
Dynamical spectrum $g(\Lambda)$      409Ч412
Dynamical system      74
Dynamical systems theory      74
Eigenvalues      see "Characteristic values"
Eigenvectors      99
Electrodeposition      474Ч477
Elliptic point      283 305Ч306 438Ч439
Embedding method      375Ч389
Embedding space      375Ч389
Energy eigenvalues      415 502Ч503
Entropy, definition      356
Entropy, generalized      393Ч404
Entropy, information      409
Entropy, Kolmogorov Ч Sinai      335Ч341 404 419
Entropy, topological      406 409 414
Equilibrium point      see "Fixed point"
Ergodic, ergodicity      288 333Ч334
Eulerian viewpoint      278 453
Existence and uniqueness theorem      77
Exponential divergence      see "Divergence of nearby trajectories"
False nearest neighbors      381
Farey tree      229Ч231
Fat fractal      346
Feigenbaum numbers, $\alpha$      55Ч56 183Ч185 568Ч574
Feigenbaum numbers, $\delta$      47Ч51 574Ч578
Feigenbaum universality      568Ч578
Feigenbaum, M.      17 47Ч48
Feigenvalues      577
Feynman      433 518
Fibonacci numbers      235
Fick's law of diffusion      451
Filtering data      365Ч366
Fixed point      20Ч22 32 164
Fixed point in three dimensions      124Ч128
Fixed point in two dimensions      88Ч94 97Ч99
Fixed point, elliptic      438Ч439
Fixed point, hyperbolic      91 148 439Ч440
Flip bifurcations      see "Period-doubling"
Floquet matrix      131
Floquet multipliers      see "Characteristic multipliers"
Fluid flow      436Ч441
Focus      see "Node"
Fold bifurcation      see "Bifurcations saddle-node"
Forced van der Pol oscillator      244
Fourier analysis and synthesis      533Ч540
Fractal      34 57 79
Fractal basin boundary      79
Fractal dimensions      341Ч354
Fractal, definition      342
Frequency-locking      135 217
Frequency-ratio parameter      218 221
Galerkin truncation      554
Game of life      447Ч448
Gaussian map      192Ч197
Generalized correlation sum      389 393 408
Generalized dimensions      see "Dimensions generalized"
Generalized entropies      see "Entropy generalized"
Gibbs      71
Ginzburg Ч Landau equation      469
Glass Ч Mackey model      512
Global bifurcation      122 541 545
Global phase portrait      85
Golden mean      231Ч234
Granular flow      441Ч442
Hamilton's equations      274
Hamiltonian function      274Ч276 437Ч438 494Ч496
Hamiltonian system      272Ч313
harmonic oscillator      see "Oscillator harmonic"
Hausdorff dimension      354 383
Heartbeat experiment      241Ч242
Heaviside step function      356
Heisenberg uncertainty relation      497
Hele-Shaw cell      475
Henon map      198
Henon Ч Heiles model      296Ч303
Heteroclinic connection      142
Heteroclinic intersection      140
Heteroclinic orbit      138Ч146
Heteroclinic point      140
Heteroclinic tangle      141Ч142 146Ч148 440
Homoclinic connection      141
Homoclinic intersection      140
Homoclinic orbit      138Ч146
Homoclinic point      140
Homoclinic tangle      141Ч142 146Ч147 440
Hopf bifurcation      111Ч113 137
Hopf bifurcation and intermittency      259
Horseshoe map      199Ч204
Horseshoe, connection to chaotic behavior      146Ч148
Husimi distribution      501
Hydrodynamic derivative      278
Hyperbolic fixed point      91 148
Hyperbolic point (for Hamiltonian systems)      287 439Ч440
Hyperchaos      150
Hysteresis      199 580
Images of the critical point      181
In-set      90Ч91
Incommensurate frequencies      211
Index of a fixed point      126
Information and chaos      513Ч514
Information, definition      513
Information, dimension      392 409
Information, entropy      409
Initial condition      see "Divergence of nearby trajectories"
Integrable system      273 279Ч289
Interior crisis      260Ч267
Intermittency      250Ч267
Intermittency, route      122 138 250Ч260
Intermittency, Type I, II, III      122 250Ч260
Invariant distribution      see "Invariant measure"
Invariant manifold      90
Invariant measure      330Ч335
Invariant measure for Bernoulli shift map      334Ч335
Invariant measure for logistic map      334Ч335
Invariant tori      288
Invertible map      198
Irrational number      188Ч189 211
Irrational ratio of frequencies      211
Islands in Hamiltonian systems      302 305Ч306
Iterated map      19Ч20 22 157Ч163 444Ч445
Jacobian matrix      97Ч100 131
Julia set      65 353
Jump time      384Ч386
KAM (Kolmogorov Ч Arnold Ч Moser) surface and tori      291Ч292 294 306Ч307 440Ч441 500Ч501
KAM (Kolmogorov Ч Arnold Ч Moser) theorem      290Ч291
Kaplan Ч Yorke conjecture      382
Karhunen Ч Loeve decomposition      479
Kneading sequence      174
Koch curve      346Ч347
Koch snowflake      347
Kolmogorov Ч Sinai (K-S) entropy      335Ч341 404 419
Kolmogorov Ч Sinai (K-S) entropy, relationship to Lyapunov exponents      339 419
Lagrangian viewpoint      278 453
Landau scenario      215
Laplace      38Ч39
Laplacian      452Ч455
Laser dynamics      598Ч604
Legendre transformation      397 410
Lifted state space      109
Limit cycle      87 96 102Ч106
Limit cycle, attracting (stable)      103 111 132Ч133
Limit cycle, repelling (unstable)      103 111 132Ч133
Limit cycle, stability      102Ч106 132
Linear systems      4Ч6
Liouville theorem      277Ч279
Local bifurcations      121Ч122
Logistic differential equation      86
Logistic map      19Ч26 47Ч57 192
Logistic map, bifurcation diagram      25
Logistic map, chaotic bands      24Ч25
Logistic map, invariant measure      332
Logistic map, Misiurewicz point      181
Lorenz model      27Ч37 145 547Ч558
Lorenz, E.      27 38
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