## Chaos Theory TamedIn this fascinating trek through the concept of chaos, Williams uses friendly language to help readers understand the vocabulary and significance of chaos theory in our lives. The book will help scientists, students, and others outside mathematics use the concepts of chaos in working with data, and it will give lay readers a foothold on the fundamentals of this new realm of thought. |

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### Contents

Chaos in perspective | 9 |

THE AUXILIARY TOOLKIT | 21 |

Distances and lines in space | 35 |

Vectors | 49 |

Probability and information | 65 |

Autocorrelation | 97 |

Fourier analysis | 107 |

The parameter as king | 161 |

Uncovering determinism | 247 |

Attractor reconstruction | 265 |

DIMENSIONS | 289 |

Similarity dimension | 301 |

Capacity and Hausdorff dimension | 315 |

Information dimension | 321 |

Correlation dimension | 329 |

QUANTITATIVE MEASURES OF CHAOS | 351 |

Nonchaotic attractors | 175 |

Routes to chaos | 189 |

Chaotic equations | 203 |

CHARACTERISTICS OF CHAOS | 209 |

The chaotic strange attractor | 221 |

Order within chaos | 229 |

Fractal structure | 237 |

KolmogorovSinai entropy | 381 |

Mutual information and redundancy | 407 |

Epilogue | 443 |

473 | |

485 | |

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### Common terms and phrases

abscissa asymptotic autocorrelation autocovariance axes axis basic bins calculations chaos theory chaotic attractor Chapter coefficients computed conditional entropy constant control parameter coordinates correlation dimension correlation sum correlogram curve data points dataset defined deterministic discrete distance dynamical system embedding dimension equal estimate example Figure Fourier analysis fractal function graph harmonic Hence increases incremental redundancy initial conditions instance interval iterations joint entropy joint probability K-S entropy lag space limit cycle linear logistic equation Lyapunov exponents mathematical means measure method moving average mutual information neighboring trajectories noise nonchaotic nonlinear number of observations number of possible period-doubling periodicity phase space plot Poincare section predictions probability distribution pseudo phase space radius random range ratio reconstruction relation routes ruler length scale scaling ratio seasonality self-entropy sequence probabilities shows slope standard statistical step straight line symbol there's total number trend variable variance vector versus wavelength weighted width zero

### References to this book

Into the Cool: Energy Flow, Thermodynamics, and Life Eric D. Schneider,Dorion Sagan No preview available - 2005 |