Index 729 diagonalizable, 714 diffeomorphism, 167, 564 differentiably conjugate, 407 dimension box, 671 correlation, 681 fractal, 670 Hausdorff, 670 Lyapunov, 682 similarity, 678 direction fields, 129 dissipative, 183 distance, 712 distance from a point to a set, 710 divergence, 243 double-well potential, 174 doubling map, 337, 356, 439 doubling the periods, 433, 436 Duﬃng equation, 200 forced, 317 Dulac criterion, 248 dynamical systems, xviii eigenvalue, 543, 713 eigenvalues of a fixed point, 137 eigenvector, 543 electric circuit, 264 elliptic center, 30 energy, 173 epidemic model, 156, 158, 589 -chain, 493, 631, 638, 665 equilibrium point, 4, 81, 120 equivalent flows, 167 Euler method, 85 higher dimensions, 91 eventually positive stochastic matrix, 581 evolutionary game theory, 202 expanding factor, 467 expanding, piecewise, 467 Feigenbaum constant, 402 Feigenbaum, M., xix, 400 Fibonacci recurrence relation, 472, 474 first return map, 216 first variation equation, 82, 102 fixed point, 4, 81, 119, 120, 354 fixed point for iteration, 356 flour beetle, 349, 586 flow, 77, 80 folding, 454 food chain, 190 forced Duﬃng equation, 317 forced oscillator, 317 forward orbit, 355 fractal, 669 fractal dimension, 670 frequency measure, 524 frequency plot, 528 friction, 183 full shift on N-symbols, 442 full shift on two symbols, 603 full shift space on two symbols, 637 full two-sided shift on finite number of symbols, 622 fundamental domain, 421 fundamental matrix solution, 15 fundamental set of solutions, 15 game theory, evolutionary, 202 generalized eigenvector, 714 generalized eigenvectors, 68 generic, 717 geometric horseshoe, 598 geometric series, 437 Gleick, J., xx globally asymptotically stable, 115, 128 gradient, 196 gradient system of differential equations, 196 graph of a function, 358 graphical method of iteration, 365 Grassberger, P., 680 Grobman–Hartman Theorem, 596 Gronwall’s inequality, 101 Hamiltonian differential equations, xix hard spring, 200 harmonic oscillator coupled, 45 damped, 49 uncoupled, 44 Hartman Theorem, 596 harvesting, 125 Hausdorff dimension, 670 Hayashi, S., 718 H´ enon attractor, 350 H´ enon map, 350, 561, 566, 571, 624, 636, 646, 649, 653, 675, 681, 682 H´ enon, M., 350 Herman, M., xix heteroclinic orbit, 178, 179 Heun method, 86 higher dimensions, 92

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