Index 731 Markov partition, 466, 621 Markov rectangles, 621 Mathematica, 25, 89, 129, 177 Mather, J., 663 Matlab, 25, 89, 129, 177 matrix of partial derivatives, 82, 137, 557, 706 May, R., xix, 345 McGehee, R., 663 measure, 515 Borel, 515 frequency, 524 Lebesgue, 516 natural, 527, 656 measure preserving, 517 metastasis of tumor cells, 52 metric, 442 metric space, 689, 712 middle-third Cantor set, 457 Milnor attractor, 289, 494 Milnor, J., 289, 494 mod, 70, 254, 356 modulo, 70, 254, 356 Moser, J., xix, 662 natural measure, 527, 656 negatively invariant, 112 neighborhood, 524, 709 neural network, 208 Newton map, 348, 373, 585 Newton method for roots, 347 Newton, I., xvii node, 26 nonhomogeneous linear system, 49 nonlinear center, 170, 180 nonrectifiable, 688 nonresonance, 596 norm of a matrix, 61, 554, 716 nowhere dense, 482, 710 nullclines, 126 numerical methods, 84 ω-limit set, 110, 488 one degree of freedom, 173 one to one, 406, 564 onto, 406 open, 286, 492, 709 open ball, 286, 555, 708 orbit, 80, 355, 565 forward, 355 periodic, 356 orbitally ω-attracting, 214 orbitally asymptotically stable, 214, 262 orbitally L-stable, 214, 262 Oregonator system, 263 oscillator, 173 coupled harmonic, 45 forced, 317 uncoupled harmonic, 44 undamped nonlinear, 200 Oseledec Multiplicative Ergodic Theorem, 656 Ottino, J., 537 partition, 428 pendulum, 177 with damping, 184 perfect, 482, 711 period, 5, 81, 214, 356 period doubling bifurcation, 397 period doubling cascade, 399 period-n point for iteration, 356 periodic, 5, 214 periodic orbit, 5, 81, 214 stable, 256 periodic point, 356 periodic sink, 214, 556 periodic source, 215 permutation matrix, 472 Perron–Frobenius operator, 529 Perron–Frobenius theorem, 520 phase plane, 23 phase portrait, 23, 126, 129 phase space, 23 Picard iteration scheme, 77, 99 piecewise expanding, 467 Poincar´ e map, 216, 217, 231, 251, 255, 273 Lorenz equations, 307 Poincar´ e, H., xvii, 636, 662 Poincar´ e–Bendixson theorem, 219 populations, 150, 412, 477 competitive, 145 epidemic, 156, 158, 589 food chain, 190 Hassel model, 413 predator–prey, 169, 241, 265 Ricker model, 413, 416, 477 SIR model, 156, 158 SIS model, 589 Verhulst model, 412 positively invariant, 112, 379, 439 potential energy, 173 predator–prey system, 169, 241, 265
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