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Generating Families in the Restricted Three-Body Problem

II. Quantitative Study of Bifurcations

  • Book
  • © 2001

Overview

Authors:
  1. Michel Hénon

    1. Observatoire de la Côte d’Azur, CNRS, Nice Cédex 4, France

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  • This is an in-depth study of an important model of a non-integrable Hamiltonian dynamical system
  • It will certainly trigger a host of interesting future research
  • Includes supplementary material: sn.pub/extras

Part of the book series: Lecture Notes in Physics Monographs (LNPMGR, volume 65)

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Table of contents (13 chapters)

  1. Front Matter

    Pages I-XII
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  2. Definitions and General Equations

    Pages 1-16

  3. Quantitative Study of Type 1

    Pages 17-38

  4. Partial Bifurcation of Type 1

    Pages 39-78

  5. Total Bifurcation of Type 1

    Pages 79-91

  6. The Newton Approach

    Pages 93-129

  7. Proving General Results

    Pages 131-148

  8. Quantitative Study of Type 2

    Pages 149-179

  9. The Case 1/3 < v < 1/2

    Pages 181-197

  10. Partial Transition 2.1

    Pages 199-224

  11. Total Transition 2.1

    Pages 225-238

  12. Partial Transition 2.2

    Pages 239-269

  13. Total Transition 2.2

    Pages 271-281

  14. Bifurcations 2T1 and 2P1

    Pages 283-296

  15. Back Matter

    Pages 297-301
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Keywords

About this book

The classical restricted three-body problem is of fundamental importance because of its applications in astronomy and space navigation, and also as a simple model of a non-integrable Hamiltonian dynamical system. A central role is played by periodic orbits, of which many have been computed numerically. This is the second volume of an attempt to explain and organize the material through a systematic study of generating families, the limits of families of periodic orbits when the mass ratio of the two main bodies becomes vanishingly small. We use quantitative analysis in the vicinity of bifurcations of types 1 and 2. In most cases the junctions between branches can now be determined. A first-order approximation of families of periodic orbits in the vicinity of a bifurcation is also obtained. This book is intended for scientists and students interested in the restricted problem, in its applications to astronomy and space research, and in the theory of dynamical systems.

Authors and Affiliations

  • Observatoire de la Côte d’Azur, CNRS, Nice Cédex 4, France

    Michel Hénon

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