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Table of contents (97 chapters)
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Front Matter
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Lectures
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Front Matter
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Keywords
About this book
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.
Editors and Affiliations
Bibliographic Information
Book Title: Hamiltonian Systems with Three or More Degrees of Freedom
Editors: Carles Simó
Series Title: Nato Science Series C:
DOI: https://doi.org/10.1007/978-94-011-4673-9
Publisher: Springer Dordrecht
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eBook Packages: Springer Book Archive
Copyright Information: Springer Science+Business Media Dordrecht 1999
Hardcover ISBN: 978-0-7923-5710-0Published: 30 June 1999
Softcover ISBN: 978-94-010-5968-8Published: 05 November 2012
eBook ISBN: 978-94-011-4673-9Published: 06 December 2012
Series ISSN: 1389-2185
Edition Number: 1
Number of Pages: XXIV, 658
Topics: Global Analysis and Analysis on Manifolds, Applications of Mathematics, Classical Mechanics, Ordinary Differential Equations, Partial Differential Equations