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Integrable Hamiltonian Systems

2004-02-25 Mathematics
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Release : 2004-02-25
Genre : Mathematics
Kind : eBook
Book Rating : 429/5 ( reviews)

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Book Synopsis Integrable Hamiltonian Systems by : A.V. Bolsinov

Download or read book Integrable Hamiltonian Systems written by A.V. Bolsinov. This book was released on 2004-02-25. Available in PDF, EPUB and Kindle. Book excerpt: Integrable Hamiltonian systems have been of growing interest over the past 30 years and represent one of the most intriguing and mysterious classes of dynamical systems. This book explores the topology of integrable systems and the general theory underlying their qualitative properties, singularites, and topological invariants. The authors,

Nearly Integrable Infinite-Dimensional Hamiltonian Systems

2006-11-15 Mathematics
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Release : 2006-11-15
Genre : Mathematics
Kind : eBook
Book Rating : 201/5 ( reviews)

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Book Synopsis Nearly Integrable Infinite-Dimensional Hamiltonian Systems by : Sergej B. Kuksin

Download or read book Nearly Integrable Infinite-Dimensional Hamiltonian Systems written by Sergej B. Kuksin. This book was released on 2006-11-15. Available in PDF, EPUB and Kindle. Book excerpt: The book is devoted to partial differential equations of Hamiltonian form, close to integrable equations. For such equations a KAM-like theorem is proved, stating that solutions of the unperturbed equation that are quasiperiodic in time mostly persist in the perturbed one. The theorem is applied to classical nonlinear PDE's with one-dimensional space variable such as the nonlinear string and nonlinear Schr|dinger equation andshow that the equations have "regular" (=time-quasiperiodic and time-periodic) solutions in rich supply. These results cannot be obtained by other techniques. The book will thus be of interest to mathematicians and physicists working with nonlinear PDE's. An extensivesummary of the results and of related topics is provided in the Introduction. All the nontraditional material used is discussed in the firstpart of the book and in five appendices.

Symplectic Geometry of Integrable Hamiltonian Systems

2012-12-06 Mathematics
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Release : 2012-12-06
Genre : Mathematics
Kind : eBook
Book Rating : 715/5 ( reviews)

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Book Synopsis Symplectic Geometry of Integrable Hamiltonian Systems by : Michèle Audin

Download or read book Symplectic Geometry of Integrable Hamiltonian Systems written by Michèle Audin. This book was released on 2012-12-06. Available in PDF, EPUB and Kindle. Book excerpt: Among all the Hamiltonian systems, the integrable ones have special geometric properties; in particular, their solutions are very regular and quasi-periodic. This book serves as an introduction to symplectic and contact geometry for graduate students, exploring the underlying geometry of integrable Hamiltonian systems. Includes exercises designed to complement the expositiont, and up-to-date references.

Lectures on Integrable Systems

2008-09-15 Science
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Release : 2008-09-15
Genre : Science
Kind : eBook
Book Rating : 746/5 ( reviews)

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Book Synopsis Lectures on Integrable Systems by : Jens Hoppe

Download or read book Lectures on Integrable Systems written by Jens Hoppe. This book was released on 2008-09-15. Available in PDF, EPUB and Kindle. Book excerpt: Mainly drawing on explicit examples, the author introduces the reader to themost recent techniques to study finite and infinite dynamical systems. Without any knowledge of differential geometry or lie groups theory the student can follow in a series of case studies the most recent developments. r-matrices for Calogero-Moser systems and Toda lattices are derived. Lax pairs for nontrivial infinite dimensionalsystems are constructed as limits of classical matrix algebras. The reader will find explanations of the approach to integrable field theories, to spectral transform methods and to solitons. New methods are proposed, thus helping students not only to understand established techniques but also to interest them in modern research on dynamical systems.

Integrable Hamiltonian systems and spectral theory

1983-10-01 Science
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Release : 1983-10-01
Genre : Science
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Book Rating : 522/5 ( reviews)

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Book Synopsis Integrable Hamiltonian systems and spectral theory by : Jürgen Moser

Download or read book Integrable Hamiltonian systems and spectral theory written by Jürgen Moser. This book was released on 1983-10-01. Available in PDF, EPUB and Kindle. Book excerpt: These notes are based on six Fermi Lectures held at the Scuola Normale Superiore in Pisa in March and April 1981. The topics treated depend on basic concepts of classical mechanics, elementary geometry, complex analysis as well as spectral theory and are meant for mathematicians and theoretical physicists alike. These lectures weave together a number of threads from various fields of mathematics impinging on the subject of inverse spectral theory. I did not try to give an overview over this fast moving subject but rather tie various aspects together by one guiding theme: the construction of all potentials for the one-dimensional Schrödinger equation which gives rise to finite band potentials, which is done by reducing it to solving a system of differential equations. In fact, we will see that the problem of finding all almost periodic potentials having finitely many intervals as its spectrum is equivalent to the study of the geodesics on an ellipsoid. To make this connection clear we have carried together several facts from classical mechanics and from spectral theory and we give a self-contained exposition of the construction of these finite band potentials.

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