Hamiltonian Systems with Three or More Degrees of Freedom

Hamiltonian Systems with Three or More Degrees of Freedom
Author :
Publisher : Springer Science & Business Media
Total Pages : 681
Release :
ISBN-10 : 9789401146739
ISBN-13 : 940114673X
Rating : 4/5 (39 Downloads)

Book Synopsis Hamiltonian Systems with Three or More Degrees of Freedom by : Carles Simó

Download or read book Hamiltonian Systems with Three or More Degrees of Freedom written by Carles Simó and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 681 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.


Hamiltonian Systems with Three or More Degrees of Freedom Related Books

Hamiltonian Systems with Three or More Degrees of Freedom
Language: en
Pages: 681
Authors: Carles Simó
Categories: Mathematics
Type: BOOK - Published: 2012-12-06 - Publisher: Springer Science & Business Media

DOWNLOAD EBOOK

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 t
Hamiltonian Dynamical Systems
Language: en
Pages: 797
Authors: R.S MacKay
Categories: Mathematics
Type: BOOK - Published: 2020-08-17 - Publisher: CRC Press

DOWNLOAD EBOOK

Classical mechanics is a subject that is teeming with life. However, most of the interesting results are scattered around in the specialist literature, which me
Chaotic Worlds: from Order to Disorder in Gravitational N-Body Dynamical Systems
Language: en
Pages: 342
Authors: B.A. Steves
Categories: Science
Type: BOOK - Published: 2006-09-22 - Publisher: Springer Science & Business Media

DOWNLOAD EBOOK

Based on the recent NATO Advanced Study Institute "Chaotic Worlds: From Order to Disorder in Gravitational N-Body Dynamical Systems", this state of the art text
Handbook of Dynamical Systems
Language: en
Pages: 556
Authors: H. Broer
Categories: Mathematics
Type: BOOK - Published: 2010-11-10 - Publisher: Elsevier

DOWNLOAD EBOOK

In this volume, the authors present a collection of surveys on various aspects of the theory of bifurcations of differentiable dynamical systems and related top
Geography of Order and Chaos in Mechanics
Language: en
Pages: 413
Authors: Bruno Cordani
Categories: Differential equations
Type: BOOK - Published: 2024 - Publisher: Springer Nature

DOWNLOAD EBOOK

This monograph explores the dynamics in the particular but very important and significant case of quasi-integrable Hamiltonian systems, or integrable systems sl