## Chaos in Dynamical SystemsOver the past two decades scientists, mathematicians, and engineers have come to understand that a large variety of systems exhibit complicated evolution with time. This complicated behavior is known as chaos. In the new edition of this classic textbook Edward Ott has added much new material and has significantly increased the number of homework problems. The most important change is the addition of a completely new chapter on control and synchronization of chaos. Other changes include new material on riddled basins of attraction, phase locking of globally coupled oscillators, fractal aspects of fluid advection by Lagrangian chaotic flows, magnetic dynamos, and strange nonchaotic attractors. This new edition will be of interest to advanced undergraduates and graduate students in science, engineering, and mathematics taking courses in chaotic dynamics, as well as to researchers in the subject. |

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### Contents

IX | 32 |

X | 45 |

XI | 57 |

XII | 65 |

XIII | 66 |

XIV | 69 |

XV | 71 |

XVI | 77 |

XVII | 80 |

XVIII | 84 |

XIX | 85 |

XX | 89 |

XXI | 91 |

XXII | 96 |

XXIII | 98 |

XXIV | 105 |

XXV | 107 |

XXVI | 113 |

XXVII | 115 |

XXVIII | 122 |

XXIX | 129 |

XXX | 137 |

XXXI | 145 |

XXXII | 152 |

XXXIII | 161 |

XXXIV | 162 |

XXXV | 166 |

XXXVI | 168 |

XXXVII | 169 |

XXXVIII | 175 |

XXXIX | 178 |

XL | 185 |

XLI | 206 |

XLII | 212 |

XLIII | 218 |

XLIV | 228 |

XLV | 233 |

LIV | 299 |

LV | 301 |

LVI | 302 |

LVII | 304 |

LVIII | 305 |

LIX | 310 |

LX | 315 |

LXI | 330 |

LXII | 334 |

LXIII | 338 |

LXIV | 342 |

LXV | 344 |

LXVI | 345 |

LXVII | 353 |

LXVIII | 356 |

LXIX | 363 |

LXX | 367 |

LXXI | 371 |

LXXII | 373 |

LXXIII | 377 |

LXXV | 379 |

LXXVI | 381 |

LXXVII | 390 |

LXXVIII | 393 |

LXXIX | 402 |

LXXX | 409 |

LXXXI | 419 |

LXXXII | 420 |

LXXXIII | 421 |

LXXXIV | 423 |

LXXXV | 439 |

LXXXVI | 442 |

LXXXVII | 449 |

LXXXVIII | 450 |

452 | |

475 | |

### Common terms and phrases

approximation assume baker's map basin of attraction behavior box-counting dimension Cantor set chaos chaotic attractor chaotic orbits chaotic scattering chaotic set chaotic systems Chapter consider constant corresponding cubes curve defined denote density dimensional discussion dynamical system eigenvalues energy entropy equation ergodic example exponential fixed point flow fluid frequency quasiperiodic Grebogi Hamiltonian Hence Henon map horseshoe map hyperbolic illustrated in Figure increases initial conditions integrable intersection interval invariant manifold invariant set iterate Lebesgue measure logistic map Lyapunov exponents magnetic field matrix metric entropy motion natural measure Note obtain one-dimensional map oscillator parameter particle particular period doubling period three periodic orbits perturbation phase space plot problem quantum region result Schematic shown in Figure shows situation smooth solution stable and unstable surface of section symplectic synchronization tori torus trajectory two-dimensional map typical unstable manifold unstable periodic orbits variables vector versus vertical yields zero