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



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Íàçâàíèå: Chaos and nonlinear dynamics

Àâòîð: Hilborn R.C.

Àííîòàöèÿ:

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.


ßçûê: en

Ðóáðèêà: Ôèçèêà/Íåëèíåéíàÿ äèíàìèêà, Õàîñ/

Ñòàòóñ ïðåäìåòíîãî óêàçàòåëÿ: Ãîòîâ óêàçàòåëü ñ íîìåðàìè ñòðàíèö

ed2k: ed2k stats

Èçäàíèå: 2nd edition

Ãîä èçäàíèÿ: 2000

Êîëè÷åñòâî ñòðàíèö: 650

Äîáàâëåíà â êàòàëîã: 10.09.2005

Îïåðàöèè: Ïîëîæèòü íà ïîëêó | Ñêîïèðîâàòü ññûëêó äëÿ ôîðóìà | Ñêîïèðîâàòü ID
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Ïðåäìåòíûé óêàçàòåëü
$f(\alpha)$ spectrum      393—404
$g(\Lambda)$      404—412
1/f noise      256 479
action      280—285 491 505—506
Action-angle variables      280—289
algorithmic complexity      508—510
Antimonotonicity      197
Area preserving maps      303—309
Arnold cat map      308—309 499
Arnold diffusion      294
Arnold tongues      225 231 372
Asymptotically stable      164
Attracting set      see "Attractor(s)"
Attractor(s)      22 32 67 78—79
Attractor(s), chaotic, defined      172
Attractor(s), strange, defined      342
Autocorrelation function      383—384
Autocorrelation time      383—388
Autonomous system      76
Average Lyapunov exponent      172 324 419
Averaging method      592—596
Baker's transformation      208
Band merging      194
Bare winding number      221
Basin boundaries      79 352—353
Basin of attraction      22 32 79 107
Benard      See "Rayleigh — Benard"
Bernoulli shift      190—192
Bifurcation      166—171
Bifurcation diagram      11 15—18 24—25 107—108
Bifurcation diagram, diode circuit      17—18
Bifurcation diagram, Gaussian map      194—196
Bifurcation diagram, Henon map      200
Bifurcation diagram, logistic map      24—25 48 58 59 180 263
Bifurcation diagram, sine-circle map      237—238
Bifurcation theory      106—113 541—546
Bifurcation, defined      11—12
Bifurcation, global      122 541 545
Bifurcation, Hopf      111—113 137
Bifurcation, local      121—122
Bifurcation, pitchfork      see "Period-doubling"
Bifurcation, point      106—113
Bifurcation, saddle-node      109
Bifurcation, tangent      109 254—256 259
Billiards      311
Biological models and noise      243—244
Birkhoff series      281
Bouncing ball model      517
Boundary crisis      260—262
Bounded system      85
Boussinesq approximation      550
Box-Counting Dimension      342—344 390
Brusselator model      100 109—110
Butterfly effect      38
Canonical transformation      280—282
Cantor set      344—345
Cantor set, asymmetric and weighted      398—402
Capacity dimension      see "Boxcounting dimension"
Cardiac cells      241—242
Cat map      308—309
Cellular automata      445—448
Center (fixed point)      see "Elliptic point"
Center manifold      543
Chaos      3—9
Chaos, criteria for      150 172
Chaos, definition      6—7
Chaotic attractor      120
Chaotic bands      25 179—182
Chaotic scattering      479
Chaotic transients      67 118 122 145
Characteristic direction      88 91 99
Characteristic equation      93 97—98
Characteristic exponent      105—106
Characteristic multiplier      105 113 132
Characteristic value      80—81 84 94 99
Chemical reactions      91
Chirikov standard map      304—307
Circle map      219—227
Cluster of initial conditions      86—87 96 150—152 159—160
Codimension      541
Coexistence of regular and chaotic motion      289—292 299—303
Coherent structures      435
Commensurate frequencies      211
Comparison time      384
Complex eigenvalues      94—96
complexity      39 434—435 490
Composition rule      169 573
Computer networks      514—515
Computer programs      64—66 560—567
Computers and chaos      61—63
Conservative system      272—273
Constant energy surface      276
Continued fractions      231—234
Continuity equation      452
Control parameter      11 15 30
Controlling chaos      515—516
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      442—445
Crisis      122 138 260—268
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      72—74 274 276
Delay-differential equation      490
Dendrites      473
Determinant      98—100
Determinism      3 6 37—39
Deterministic chaos      6
Devil's staircase      227
Diffusion      450—456
Diffusion-limited aggregation      471—474
Dimensions, box-counting      342 390
Dimensions, correlation      354—368 392—394
Dimensions, fractal      341—354
Dimensions, generalized      389 390 392—394
Dimensions, Hausdorff      354 383
Dimensions, information      392 409
Dimensions, Lyapunov      383
Dimensions, pointwise      359
Dimensions, similarity      348—352
Dimensions, topological      354
Diode circuit      8—17 51—52 160—161 510—511
dispersion relation      465
Dissipation      see also "Dissipative systems"
Dissipation and Jacobian      97—99
Dissipation and sum of Lyapunov exponents      148—152
Dissipative standard map      309—311
Dissipative systems      78—79 86—87
Divergence of nearby trajectories      13—14 16 25 37—39 172
Divergence theorem and dissipation      87 96—97
Double crisis      267
Doubling transformation      574
Drift ring      214 227
Duffing oscillator      71 579—583
Dynamical localization      507
Dynamical partition function      416
Dynamical spectrum $g(\Lambda)$      409—412
Dynamical system      74
Dynamical systems theory      74
Eigenvalues      see "Characteristic values"
Eigenvectors      99
Electrodeposition      474—477
Elliptic point      283 305—306 438—439
Embedding method      375—389
Embedding space      375—389
Energy eigenvalues      415 502—503
Entropy, definition      356
Entropy, generalized      393—404
Entropy, information      409
Entropy, Kolmogorov — Sinai      335—341 404 419
Entropy, topological      406 409 414
Equilibrium point      see "Fixed point"
Ergodic, ergodicity      288 333—334
Eulerian viewpoint      278 453
Existence and uniqueness theorem      77
Exponential divergence      see "Divergence of nearby trajectories"
False nearest neighbors      381
Farey tree      229—231
Fat fractal      346
Feigenbaum numbers, $\alpha$      55—56 183—185 568—574
Feigenbaum numbers, $\delta$      47—51 574—578
Feigenbaum universality      568—578
Feigenbaum, M.      17 47—48
Feigenvalues      577
Feynman      433 518
Fibonacci numbers      235
Fick's law of diffusion      451
Filtering data      365—366
Fixed point      20—22 32 164
Fixed point in three dimensions      124—128
Fixed point in two dimensions      88—94 97—99
Fixed point, elliptic      438—439
Fixed point, hyperbolic      91 148 439—440
Flip bifurcations      see "Period-doubling"
Floquet matrix      131
Floquet multipliers      see "Characteristic multipliers"
Fluid flow      436—441
Focus      see "Node"
Fold bifurcation      see "Bifurcations saddle-node"
Forced van der Pol oscillator      244
Fourier analysis and synthesis      533—540
Fractal      34 57 79
Fractal basin boundary      79
Fractal dimensions      341—354
Fractal, definition      342
Frequency-locking      135 217
Frequency-ratio parameter      218 221
Galerkin truncation      554
Game of life      447—448
Gaussian map      192—197
Generalized correlation sum      389 393 408
Generalized dimensions      see "Dimensions generalized"
Generalized entropies      see "Entropy generalized"
Gibbs      71
Ginzburg — Landau equation      469
Glass — Mackey model      512
Global bifurcation      122 541 545
Global phase portrait      85
Golden mean      231—234
Granular flow      441—442
Hamilton's equations      274
Hamiltonian function      274—276 437—438 494—496
Hamiltonian system      272—313
harmonic oscillator      see "Oscillator harmonic"
Hausdorff dimension      354 383
Heartbeat experiment      241—242
Heaviside step function      356
Heisenberg uncertainty relation      497
Hele-Shaw cell      475
Henon map      198
Henon — Heiles model      296—303
Heteroclinic connection      142
Heteroclinic intersection      140
Heteroclinic orbit      138—146
Heteroclinic point      140
Heteroclinic tangle      141—142 146—148 440
Homoclinic connection      141
Homoclinic intersection      140
Homoclinic orbit      138—146
Homoclinic point      140
Homoclinic tangle      141—142 146—147 440
Hopf bifurcation      111—113 137
Hopf bifurcation and intermittency      259
Horseshoe map      199—204
Horseshoe, connection to chaotic behavior      146—148
Husimi distribution      501
Hydrodynamic derivative      278
Hyperbolic fixed point      91 148
Hyperbolic point (for Hamiltonian systems)      287 439—440
Hyperchaos      150
Hysteresis      199 580
Images of the critical point      181
In-set      90—91
Incommensurate frequencies      211
Index of a fixed point      126
Information and chaos      513—514
Information, definition      513
Information, dimension      392 409
Information, entropy      409
Initial condition      see "Divergence of nearby trajectories"
Integrable system      273 279—289
Interior crisis      260—267
Intermittency      250—267
Intermittency, route      122 138 250—260
Intermittency, Type I, II, III      122 250—260
Invariant distribution      see "Invariant measure"
Invariant manifold      90
Invariant measure      330—335
Invariant measure for Bernoulli shift map      334—335
Invariant measure for logistic map      334—335
Invariant tori      288
Invertible map      198
Irrational number      188—189 211
Irrational ratio of frequencies      211
Islands in Hamiltonian systems      302 305—306
Iterated map      19—20 22 157—163 444—445
Jacobian matrix      97—100 131
Julia set      65 353
Jump time      384—386
KAM (Kolmogorov — Arnold — Moser) surface and tori      291—292 294 306—307 440—441 500—501
KAM (Kolmogorov — Arnold — Moser) theorem      290—291
Kaplan — Yorke conjecture      382
Karhunen — Loeve decomposition      479
Kneading sequence      174
Koch curve      346—347
Koch snowflake      347
Kolmogorov — Sinai (K-S) entropy      335—341 404 419
Kolmogorov — Sinai (K-S) entropy, relationship to Lyapunov exponents      339 419
Lagrangian viewpoint      278 453
Landau scenario      215
Laplace      38—39
Laplacian      452—455
Laser dynamics      598—604
Legendre transformation      397 410
Lifted state space      109
Limit cycle      87 96 102—106
Limit cycle, attracting (stable)      103 111 132—133
Limit cycle, repelling (unstable)      103 111 132—133
Limit cycle, stability      102—106 132
Linear systems      4—6
Liouville theorem      277—279
Local bifurcations      121—122
Logistic differential equation      86
Logistic map      19—26 47—57 192
Logistic map, bifurcation diagram      25
Logistic map, chaotic bands      24—25
Logistic map, invariant measure      332
Logistic map, Misiurewicz point      181
Lorenz model      27—37 145 547—558
Lorenz, E.      27 38
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