730 Index Hirsch, M., 264 histogram, 528 homeomorphism, 167, 406, 564 homoclinic bifurcation, 213, 245 homoclinic orbit, 177 homoclinic point, 636 Hopf bifurcation, 235 hyperbolic, 559 hyperbolic fixed point, 137 hyperbolic periodic orbit, 256 hyperbolic toral automorphism, 575 hyperbolicity, 612, 632 IFS, 685 image, 564 improved Euler method, 86 higher dimensions, 92 inflation, 54 initial condition, 13 input-output, 55 integral of motion, 4 interior, 286, 424, 492, 709 invariant, 112 negatively, 112 positively, 112, 379, 439 invariant measure, 517 invariant set, 439 basic, 647, 665 inverse, 564 irrational rotation, 660 irreducible, 581 irreducible transition graph, 468 irreducible transition matrix, 472 irreducible word, 429 isocline, 126 isolated invariant set, 640 isolating neighborhood, 640 iterate, 256 iterated-function system, 685 with probabilities, 692 iterates of a function, 354 itinerary, 426, 430 map, 444, 603, 629 Jordan canonical form, 67, 715 Kaplan, J., 680, 682 Keynesian IS-LM model, 58 kinetic energy, 173 King Oscar’s prize, 662 Koch curve, 687 Kolmogorov, A.N., xix, 671 Kupka–Smale property, 720 L-stable, 115, 368, 555 orbitally, 214 Lanford, O.E., 402 Lasota, A., 530 least period, 356 Lebesgue measure, 516 length of an interval, 443 Leontief, 55 level set, 174 Li, T.Y., xviii, 293, 424, 493, 498, 530 Lienard equation, 229, 265 limit cycle, 215 limit set α-limit set, 110, 565 ω-limit set, 110, 488 linear combination, 14, 714 linear transformation, 541 linearized stability, 557 linearized system, 137 linearly conjugate, 407 linearly independent, 544, 714 linearly independent set of solutions, 15 Liouville formula, 15, 63, 248, 282, 325 Lipschitz, 97 local diffeomorphism, 595 local stable manifold, 138, 570, 608 local unstable manifold, 139 logistic differential equation, 120 logistic equation, 79 logistic function, 345, 363 Lorenz differential equations, 297 Lorenz, E., xix, 291, 331 Lotka, A.J., xix Lotka–Volterra equations, 145, 169, 201, 202, 269 Lyapunov dimension, 682 Lyapunov exponent, 321 Lyapunov function, 186, 210 weak, 186 Lyapunov stable, 115, 368, 555 M-rectangle, 613 Mandelbrot, B., 669 manifold, 139, 567, 712 local stable, 138 local unstable, 139 stable, 138, 570 unstable, 138 Maple, 25, 89, 129, 177 Markov chain, 351, 580
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