عنوان

Hamiltonian Systems with Three or More Degrees of Freedom

(Number (ISBN

9789401059688

(Number (ISBN

9789401146739

Number

b408856

Title Proper

Hamiltonian Systems with Three or More Degrees of Freedom

General Material Designation

[Book]

First Statement of Responsibility

edited by Carles Simó.

Place of Publication, Distribution, etc.

Dordrecht :

Name of Publisher, Distributor, etc.

Imprint: Springer,

Date of Publication, Distribution, etc.

1999.

Series Title

NATO ASI Series, Series C:Mathematical and Physical Sciences,

Volume Designation

533

ISSN of Series

1389-2185 ;

Text of Note

Lectures -- CONTRIBUTIONS -- List of authors.

0

Text of Note

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.

International Standard Book Number

9789401059688

Title

Springer eBooks

Parallel Title

Proceedings of the NATO Advanced Study Institute, S'Agaro, Spain, June 19-30, 1995

Differential equations, Partial.

Differential Equations.

Global analysis.

Mathematics.

Mechanics.

Simó, Carles.

SpringerLink (Online service)

Date of Transaction

20190301082900.0

Electronic name

[Book]

Y