Nato Science Series C:

Hamiltonian Systems with Three or More Degrees of Freedom

Editors: Simó, Carles (Ed.)

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eBook 296,31 €
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  • ISBN 978-94-011-4673-9
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Hardcover 369,20 €
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Softcover 369,20 €
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  • ISBN 978-94-010-5968-8
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About this book

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.

Table of contents (97 chapters)

  • Inflection Points, Extatic Points and Curve Shortening

    Angenent, S.

    Pages 3-10

    Preview Buy Chapter 30,19 €
  • Topologically Necessary Singularities on Moving Wavefronts and Caustics

    Arnold, Vladimir I.

    Pages 11-12

    Preview Buy Chapter 30,19 €
  • Heteroclinic Chains of Skew Product Hamiltonian Systems

    Bolotin, Sergey V.

    Pages 13-25

    Preview Buy Chapter 30,19 €
  • Order and Chaos in 3-D Systems

    Contopoulos, G. (et al.)

    Pages 26-38

    Preview Buy Chapter 30,19 €
  • Splitting of Separatrices in Hamiltonian Systems and Symplectic Maps

    Delshams, Amadeu (et al.)

    Pages 39-54

    Preview Buy Chapter 30,19 €

Buy this book

eBook 296,31 €
price for Spain (gross)
  • ISBN 978-94-011-4673-9
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover 369,20 €
price for Spain (gross)
  • ISBN 978-0-7923-5710-0
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
  • The final prices may differ from the prices shown due to specifics of VAT rules
Softcover 369,20 €
price for Spain (gross)
  • ISBN 978-94-010-5968-8
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
  • The final prices may differ from the prices shown due to specifics of VAT rules
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Bibliographic Information

Bibliographic Information
Book Title
Hamiltonian Systems with Three or More Degrees of Freedom
Editors
  • Carles Simó
Series Title
Nato Science Series C:
Series Volume
533
Copyright
1999
Publisher
Springer Netherlands
Copyright Holder
Springer Science+Business Media Dordrecht
eBook ISBN
978-94-011-4673-9
DOI
10.1007/978-94-011-4673-9
Hardcover ISBN
978-0-7923-5710-0
Softcover ISBN
978-94-010-5968-8
Series ISSN
1389-2185
Edition Number
1
Number of Pages
XXIV, 658
Topics