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From Newton to Chaos

Modern Techniques for Understanding and Coping with Chaos in N-Body Dynamical Systems

  • Book
  • © 1995

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Editors:
  1. Archie E. Roy

    1. Dept. of Physics and Astronomy, Glasgow University, Glasgow, UK

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  2. Bonnie A. Steves

    1. Dept. of Mathematics, Glasgow Caledonian University, Glasgow, UK

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    You can also search for this editor in PubMed   Google Scholar

Part of the book series: NATO Science Series B: (NSSB, volume 336)

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Table of contents (54 chapters)

  1. Front Matter

    Pages i-xvi
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  2. Poincaré’s Contributions to Chance and Chaos

    1. Poincaré’s Contributions to Chance and Chaos

      • V. Szebehely
      Pages 1-3

  3. Planetary Theory

    1. Front Matter

      Pages 4-4
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    2. Perturbation Theory: Techniques and Limitations

      • P. J. Message
      Pages 5-19

    3. Quantitative Methods in Classical Perturbation Theory

      • Antonio Giorgilli
      Pages 21-37

    4. Jacobi Geometry and Chaos in N-Body Systems

      • Piero Cipriani, Giuseppe Pucacco
      Pages 39-46

    5. Proper Elements and Stable Chaos

      • Andrea Milani
      Pages 47-78

    6. Mechanisms of Generation of Chaos in the Solar System

      • John D. Hadjidemetriou
      Pages 79-96

    7. On the Convergence of the Disturbing Function

      • S. Ferraz-Mello
      Pages 97-98

    8. Improving the Classical Expansion of the Disturbing Function

      • Tadashi Yokoyama
      Pages 99-102

    9. The Great Inequality in a Hamiltonian Planetary Theory

      • F. Varadi, M. Ghil, W. M. Kaula
      Pages 103-108

    10. Stability Over Exponentially Long Times in the Planetary Problem

      • Laurent Niederman
      Pages 109-118

    11. Interlude

      • I. P. Williams
      Pages 119-126

  4. Dynamics of Asteroids, Comets and Meteors

    1. Front Matter

      Pages 127-127
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    2. From Order to Chaos: Clustering and Diffusion Processes for Small Bodies in Solar System

      • C. Froeschlé
      Pages 129-155

    3. Depletion of the Asteroid Belt at Resonances

      • S. Ferraz-Mello, R. Dvorak, T. A. Michtchenko
      Pages 157-169

    4. On the Depletion of the Outer Asteroid Belt

      • Judit Györgyey Ries
      Pages 171-175

    5. The Chaotic Zone Connected with the 5/2 Mean Motion Resonance

      • David Nesvorný
      Pages 177-181

    6. The Influence of Chaos on the Evolution of the Minor Bodies of the Solar System

      • R. O. Vicente
      Pages 183-192

    7. Project Criss-Cross: A Preliminary Analysis

      • Othon C. Winter, Carl D. Murray
      Pages 193-198
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Keywords

About this book

The reader will find in this volume the Proceedings of the NATO Advanced Study Institute held in Cortina d' Ampezzo, Italy, between July 25 and August 6, 1993, under the title From Newton to Chaos: Modem Techniques for Understanding and Coping With Chaos inN-Body Dynamical Systems. This institute was the latest in a series of meetings held every three years from 1972 to 1990 in dynamical astronomy, theoretical mechanics and celestial mechanics. The proceedings from these institutes have been well-received in the international community of research workers in these disciplines. The present institute was well attended with 15 series of lectures being given by invited speakers: in addition some 40 presentations were made by the other participants. The majority of these contributions are included in these proceedings. The all-pervading influence of chaos in dynamical systems (of even a few variables) has now been universally recognised by researchers, a recognition forced on us by our ability, using powerful computer hardware and software, to tackle dynamical problems that until twenty-five years ago were intractable. Doubtless it was felt by many that these new techniques provided a break-through in celestial mechanics and its related disciplines. And so they were.

Editors and Affiliations

  • Dept. of Physics and Astronomy, Glasgow University, Glasgow, UK

    Archie E. Roy

  • Dept. of Mathematics, Glasgow Caledonian University, Glasgow, UK

    Bonnie A. Steves

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