## Explaining ChaosChaotic dynamics has been hailed as the third great scientific revolution in physics in this century, comparable to relativity and quantum mechanics. In this book, Peter Smith takes a cool, critical look at such claims. He cuts through the hype and rhetoric by explaining some of the basic mathematical ideas in a clear and accessible way, and by carefully discussing the methodological issues that arise. In particular, he explores the new kinds of explanation of empirical phenomena that modern dynamics can deliver. Explaining Chaos will be compulsory reading for philosophers of science and for anyone who has wondered about the conceptual foundations of chaos theory. |

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### Contents

Preface | 2 |

Fractal intricacy | 20 |

Intricacy and simplicity | 39 |

Approximate truth | 71 |

Universality | 91 |

Explanation | 113 |

Worldly chaos | 132 |

Randomness | 147 |

Defining chaos | 165 |

Notes | 185 |

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### Common terms and phrases

approximate truth arbitrarily attracting Barnsley behaviour bifurcation binary box-counting dimension Cantor set chaos theory chaotic dynamics chaotic models chaotic system claim coarse-grained complex consider convection defined definition dependence on initial deterministic differential digits dynamical model dynamical systems dynamical theories empirical example explanation fact Figure finite fixed point fluid folded back fractal function geometric structure give Hence homoclinic infinitely intricate initial conditions interlude invariant iterates KCS random kind Koch curve least length Liapunov exponents logistic map Lorenz attractor Lorenz equations Lorenz model Lorenz system mathematical models noted notion one-dimensional pair parameter pattern patternless pendulum period-doubling period-doubling bifurcation periodic orbits periodic points phase space precise predictions Rayleigh-Benard relevant result scaling sense sensitive dependence sequence set of points simple simplicity story stretching and folding suppose theorem tion topological topological entropy trajectories starting trajectory bundles true typical unit interval values variables velocity