732 Index principal Lyapunov exponents, 329 probability transition matrix, 581 Procaccia, I., 680 pseudo-orbit, 631, 665 Pugh, C., 718 quasiperiodic, 45, 52, 295, 330, 660 quasiperiodic function, 48 rationally independent, 47 reducible word, 429 repeated eigenvalues, 35 repelling fixed point, 119, 123 periodic point, 368, 556, 565 repelling fixed point, 116 repelling periodic point, 556, 565 replicator system of differential equations, 203 Ricker model, 416 rooftop map, 490 ossler attractor, 313 ossler, O., xx rotary solutions, 179 Ruelle, D., xviii, 316 Runge–Kutta method, 87 higher dimensions, 93 saddle, 24 linear map, 547 saddle fixed point, 137 saddle periodic point, 559 Sauer, T., 513, 660 scaling dimension, 678 Schwarzian derivative, 388 second-order scalar equations, 41 self-excited oscillator, 229 self-similar, 669, 684 semiconjugacy, 407 semistable, 123, 215, 368 sensitive dependence on initial conditions, xx, 8, 291, 452, 641 at points in a set, 291, 452 when restricted to a set, 291, 452 separation of variables, 77 separatrix, 567 set difference, 708 shadowed, 631 Sharkovskii ordering, 431 Sharkovskii, A. N., 424 shed map, 465 shift map, 442, 604 shift space, 468, 604 full two-sided, 622 Siegel, C. L., xix Sierpinski gasket, 686 similarity, 686 similarity dimension, 678 Sinai, Ya., 622 Sinai–Ruelle–Bowen measure, 656 Singer, D., 386 sink, 115, 368 linear map, 553 SIR model, 156, 158 SIS model, 589 Sitnikov, K., xix, 662 six-twelve potential, 200 Smale horseshoe, 598 Smale, S., xviii, 575, 598, 662, 717 soft spring, 200 solution of a linear equation, 13 source, 116, 368, 556 linear map, 553 sphere, 709 stable periodic orbit, 256 stable eigenspace, 573 stable fixed point, 115 stable focus, 32, 552 stable manifold, 115, 135, 138, 570 stable node, 26 linear map, 545 stable subspace, 139 stair step method of iteration, 365 Sternberg Theorem, 596 Stewart, I., xx stochastic matrix, 581 strange attractor, xviii, 316 stretching, 454 stretching factor, 467 string, 430 strongly attracting, 187 subcritical bifurcation, 233 subshift of finite type, 465, 468, 471, 622, 637 superattracting, 369, 586 supercritical bifurcation, 233 support of a measure, 515 symbol space, 442, 603, 604 symbolic dynamics, 423 symbols, 428 Takens, F., xviii, 316 tangent space to a manifold, 719
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