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Hamiltonian Systems with Three or More Degrees of Freedom

  • Carles Simó

Part of the NATO ASI Series book series (ASIC, volume 533)

Table of contents

  1. Front Matter
    Pages i-xxiv
  2. Lectures

    1. Front Matter
      Pages 1-1
    2. G. Contopoulos, N. Voglis, C. Efthymiopoulos
      Pages 26-38
    3. Amadeu Delshams, Rafael Ramírez-Ros, Tere M. Seara
      Pages 39-54
    4. Giovanni Gallavotti
      Pages 62-71
    5. Philip Boyland, Christophe Golé
      Pages 90-114
    6. Jacques Laskar
      Pages 134-150
    7. Angel Jorba, Rafael De La Llave, Maorong Zou
      Pages 151-167
    8. Dmitry V. Treschev
      Pages 244-253
  3. Contributions

    1. Front Matter
      Pages 283-283
    2. A. Bazzani, F. Brini
      Pages 300-304
    3. F. Borondo, R. Guantes, J. Bowers, Ch. Jaffé, S. Miret-Artés
      Pages 314-317
    4. T. Bountis, L. Drossos
      Pages 318-323
    5. Holger R. Dullin
      Pages 330-334
    6. N. Voglis, C. Efthymiopoulos, G. Contopoulos
      Pages 340-344
    7. L. Chierchia, C. Falcolini
      Pages 345-349
    8. Yuri N. Fedorov
      Pages 350-356
    9. Sebastián Ferrer, Jesús Palacián, Patricia Yanguas, M. Lara
      Pages 362-366
    10. Amadeu Delshams, Àngel Jorba, Tere M. Seara, Vassili Gelfreich
      Pages 367-371
    11. Guido Gentile, Vieri Mastropietro
      Pages 372-376
    12. C. Grotta Ragazzo
      Pages 377-385
    13. P. G. Hjorth
      Pages 408-412

About this book

Introduction

A survey of current knowledge about Hamiltonian systems with three or more degrees of freedom and related topics. The Hamiltonian systems appearing in most of the applications are non-integrable. Hence methods to prove non-integrability results are presented and the different meaning attributed to non-integrability are discussed. For systems near an integrable one, it can be shown that, under suitable conditions, some parts of the integrable structure, most of the invariant tori, survive. Many of the papers discuss near-integrable systems.
From a topological point of view, some singularities must appear in different problems, either caustics, geodesics, moving wavefronts, etc. This is also related to singularities in the projections of invariant objects, and can be used as a signature of these objects. Hyperbolic dynamics appear as a source on unpredictable behaviour and several mechanisms of hyperbolicity are presented. The destruction of tori leads to Aubrey-Mather objects, and this is touched on for a related class of systems. Examples without periodic orbits are constructed, against a classical conjecture.
Other topics concern higher dimensional systems, either finite (networks and localised vibrations on them) or infinite, like the quasiperiodic Schrödinger operator or nonlinear hyperbolic PDE displaying quasiperiodic solutions.
Most of the applications presented concern celestial mechanics problems, like the asteroid problem, the design of spacecraft orbits, and methods to compute periodic solutions.

Keywords

Kolmogorov–Arnold–Moser theorem Signatur degrees of freedom dynamics mechanics partial differential equation stability turbulence

Editors and affiliations

  • Carles Simó
    • 1
  1. 1.Universitat de BarcelonaBarcelonaSpain

Bibliographic information

  • DOI https://doi.org/10.1007/978-94-011-4673-9
  • Copyright Information Kluwer Academic Publishers 1999
  • Publisher Name Springer, Dordrecht
  • eBook Packages Springer Book Archive
  • Print ISBN 978-94-010-5968-8
  • Online ISBN 978-94-011-4673-9
  • Series Print ISSN 1389-2185
  • Buy this book on publisher's site