## Order and Chaos in Dynamical AstronomyThere have been many books on Dynamical Astronomy up to now. Many are devoted to Celestial Mechanics, but there are also several books on Stellar and Galactic Dynamics. The first books on stellar dynamics dealt mainly with the statistics of stellar motions (e. g. Smart's "Stellar Dynamics" (1938), or Trumpler and Weaver's "Statistical Astronomy" (1953)). A classical book in this field is Chandrasekhar's "Principles of Stellar Dynamics" (1942) that dealt mainly with the time of relaxation, the solutions of Liouville's equation, and the dynamics of clusters. In the Dover edition of this book (1960) an extended Appendix was added, containing the statistical mechanics of stellar systems, a quite "modern" subject at that time. The need for a classroom book was covered for several years by the book of Mihalas and Routly "Galactic Astronomy" (1969). But the most complete book in this field is Binney and Tremaine's "Galactic Dynamics" (1987). This book covers well the classical topics of stellar dynamics, and many subjects of current interest. Another classical book in dynamical astronomy is the extensive 4-Volume treatise of Hagihara "Celestial Mechanics" (1970, 1972, 1974, 1975). In more recent years much progress has been made on new topics that are of vital interest for stellar and galactic dynamics. The main new topic is Chaos. The progress of the theory of chaos has influenced considerably the area of stellar and galactic dynamics. The study of order and chaos has provided a new dimension in dynamics. |

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### Contents

I | 1 |

II | 2 |

III | 3 |

IV | 4 |

V | 5 |

VI | 6 |

VII | 8 |

VIII | 9 |

LXXXIV | 318 |

LXXXV | 322 |

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LXXXVII | 332 |

LXXXVIII | 335 |

LXXXIX | 339 |

XC | 344 |

XCI | 351 |

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XXX | 78 |

XXXI | 82 |

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L | 168 |

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CXLI | 529 |

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CLVII | 572 |

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CLIX | 579 |

CLX | 583 |

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### Common terms and phrases

angle appear application approximately asymptotic curves axis becomes bifurcations calculations called central chaos chaotic chaotic domain chaotic orbits characteristic close completely considered constant contains Contopoulos corotation corresponding defined degrees of freedom density deviation diffusion dimension direct distribution dynamical energy equal equation escape et al example exist fact frequencies function further galaxy gaps given gives Hamiltonian hand important increases infinite infinity initial inside integral intersections invariant curves islands larger limiting lobes Lyapunov method motion namely original parameter particles particular periodic orbits perturbation phase space plane points positive potential problem produce region represents resonance respect Sect similar smaller solution spectrum spiral stable surface of section theorem theory third integral unstable unstable periodic orbits variables various zero

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Page 590 - Bleher S, Ott E and Grebogi C 1989 Phys. Rev. Lett. 63 919 Bleher S, Grebogi C and Ott E 1990 Physica 46D 87 [13] Kovacs Z and Tel T 1990 Phys.

Page 587 - Applegate, JH, Douglas, MR, Gursel, Y., Hunter, P., Seitz, C. and Sussman. GJ: 1985, IEEE Trans.