## Chaos and Complexity in AstrophysicsThe discipline of nonlinear dynamics has developed explosively in all areas of physics over the last two decades. This comprehensive primer summarizes the main developments in the mathematical theory of dynamical systems, chaos, pattern formation and complexity. An introduction to mathematical concepts and techniques is given in the first part of the book, before being applied to stellar, interstellar, galactic and large scale complex phenomena in the Universe. Oded Regev demonstrates the possible application of ideas including strange attractors, Poincaré sections, fractals, bifurcations, and complex spatial patterns, to specific astrophysical problems. |

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### Contents

Introduction to Part I | 3 |

Mathematical properties of dynamical systems | 40 |

Properties of chaotic dynamics | 112 |

Analysis of time series | 146 |

Regular and irregular motion in Hamiltonian systems | 168 |

Extended systems instabilities and patterns | 201 |

Introduction to Part II | 257 |

Irregularly variable astronomical point sources | 317 |

Complex spatial patterns in astrophysics | 347 |

Topics in astrophysical fluid dynamics | 381 |

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### Common terms and phrases

accretion accretion disc analysis analytical approach astrophysical attractor basic bifurcation boundary conditions calculations chaos chaotic behaviour Chapter complex consider constant convection corresponding curve defects defined depends derived detail dimensional discrete discussion dissipative dynamical system eigenvalues energy equilibrium evolution example finite fixed point flow fluid dynamics Fourier fractal dimension frequency function galaxy gravitational Hamiltonian systems homoclinic Hopf bifurcation initial conditions instability integrable invariant iterations Lagrangian Liapunov exponents Liapunov functional limit cycle linear stability logistic map low-dimensional manifold mass mathematical modes nonlinear obviously one-dimensional orbital dynamics orbits original oscillator parameter particle periodic perturbation phase space physical planets Poincare map potential problem properties pulsation quasiperiodic Regev relevant resonances rotating scales signal solution spatial stability matrix stable stars stellar structure surface of section term theorem theory thermal timescale tion tori torus trajectories transformation turbulence two-dimensional unstable manifolds variables vector velocity zero