Alligood K., Sauer T., Yorke J.A. Chaos: An Introduction to Dynamical Systems
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I NDEX
singular value decomposition, 565
sink, 10, 10, 11, 58, 60, 68, 70,
281
periodic, 15
sinks
coexisting, 132
skinny baker map, 157, 196, 213,
223
slope field, 280
Smale, S., 216, 410
smooth, 10
snake, 522
solar system, 99, 101
solenoid map, 243
solid torus, 243
source, 10, 58, 68, 70, 76, 281
periodic, 15
specific heat, 44
squid axon, 356
stability shedding, 519
stable
asymptotically, 290, 307
equilibrium point, 290
globally asymptotically, 389
Lyapunov, 290, 306
stable manifold, 48, 78, 399, 436
local, 422
Stable Manifold Theorem, 440
standard map, 475, 478
state, 44, 538
state space, 44
steady state, 105
stick and socket model, 504, 517
stochastic process, 2
stretching factor, 245
stretching partition, 245
stroboscopic, 49
subharmonic, 533
superstable, 37, 527
surface of section, 49
swingby, 103
symbol sequences, 127, 137
for W-map, 246
symbol space, 124
symmetric matrix, 563
symmetry, 459
synchronization, 387
applied to communication, 392
of lasers, 397
tangent line, 60
Taylor’s Theorem, 424, 529
Taylor-Couette flow, 188
tent map, 36, 112, 161
congugacy, 116
Lyapunov exponent of, 114
ternary expansion, 152
three-body problem, 46, 49, 103, 225
restricted, 48
three-headed coin, 157
time series, 538
time-T map, 44, 277
Jacobian matrix of, 382, 390
tinker toy, 504
Tinkerbell map, 199
topological embedding, 543
torus, 92, 348
irrational flow, 386
total energy
for pendulum, 300
trace, 95, 384
trajectory segments, 342
transient, 106
transient chaos, 365, 369, 421
transition graph, 30, 33, 36, 112, 125, 136,
146, 247
transitivity, 340
transpose, 563
transversal, 341
crossing, 411
trapping region, 242, 308, 366, 368, 434
Tribolium, 39
two-way coupling, 387
uncertainty exponent, 184
uncountable, 153
unimodal, 32
uniqueness, 296
of solutions, 280
universality, 502, 526
unstable manifold, 48, 78, 399, 436
numerical calculation, 407
602
I NDEX
Van der Pol equation, 316, 323
variational equation, 382, 390
vector field
on torus, 349
vertically aligned, 425
W-map, 241, 257
Wada basin, 438
weak coupling, 389, 396
weather forecasting, 359
Whitney Embedding Theorem, 546
Yoneyama, M., 432
Z-matrix, 258
603