Spinning Tops

A Course on Integrable Systems

Author: M. Audin

Publisher: Cambridge University Press

ISBN: 9780521779197

Category: Mathematics

Page: 148

View: 950

Since the time of Lagrange and Euler, it has been well known that an understanding of algebraic curves can illuminate the picture of rigid bodies provided by classical mechanics. A modern view of the role played by algebraic geometry has been established iby many mathematicians. This book presents some of these techniques, which fall within the orbit of finite dimensional integrable systems. The main body of the text presents a rich assortment of methods and ideas from algebraic geometry prompted by classical mechanics, whilst in appendices the general, abstract theory is described. The methods are given a topological application to the study of Liouville tori and their bifurcations. The book is based on courses for graduate students given by the author at Strasbourg University but the wealth of original ideas will make it also appeal to researchers.
Posted in Mathematics

Integrable Systems in the Realm of Algebraic Geometry

Author: Pol Vanhaecke

Publisher: Springer Science & Business Media

ISBN: 3540423370

Category: Mathematics

Page: 264

View: 7405

This book treats the general theory of Poisson structures and integrable systems on affine varieties in a systematic way. Special attention is drawn to algebraic completely integrable systems. Several integrable systems are constructed and studied in detail and a few applications of integrable systems to algebraic geometry are worked out. In the second edition some of the concepts in Poisson geometry are clarified by introducting Poisson cohomology; the Mumford systems are constructed from the algebra of pseudo-differential operators, which clarifies their origin; a new explanation of the multi Hamiltonian structure of the Mumford systems is given by using the loop algebra of sl(2); and finally Goedesic flow on SO(4) is added to illustrate the linearizatin algorith and to give another application of integrable systems to algebraic geometry.
Posted in Mathematics

Integrable Systems, Topology, and Physics

A Conference on Integrable Systems in Differential Geometry, University of Tokyo, Japan, July 17-21, 2000

Author: Joel B Wolfe,Martin A. Guest,Reiko Miyaoka,Yoshihiro Ohnita

Publisher: American Mathematical Soc.

ISBN: 0821829394

Category: Mathematics

Page: 324

View: 5134

Ideas and techniques from the theory of integrable systems are playing an increasingly important role in geometry. Thanks to the development of tools from Lie theory, algebraic geometry, symplectic geometry, and topology, classical problems are investigated more systematically. New problems are also arising in mathematical physics. A major international conference was held at the University of Tokyo in July 2000. It brought together scientists in all of the areas influenced by integrable systems. This book is the second of three collections of expository and research articles. This volume focuses on topology and physics. The role of zero curvature equations outside of the traditional context of differential geometry has been recognized relatively recently, but it has been an extraordinarily productive one, and most of the articles in this volume make some reference to it.Symplectic geometry, Floer homology, twistor theory, quantum cohomology, and the structure of special equations of mathematical physics, such as the Toda field equations - all of these areas have gained from the integrable systems point of view and contributed to it. Many of the articles in this volume are written by prominent researchers and will serve as introductions to the topics. It is intended for graduate students and researchers interested in integrable systems and their relations to differential geometry, topology, algebraic geometry, and physics. The first volume from this conference, also available from the 'AMS', is ""Differential Geometry and Integrable Systems, Volume 308"" in the ""Contemporary Mathematics"" series. The forthcoming third volume will be published by the Mathematical Society of Japan and will be available outside of Japan from the 'AMS' in the ""Advanced Studies in Pure Mathematics"" series.
Posted in Mathematics

Algebraic Integrability, Painlevé Geometry and Lie Algebras

Author: Mark Adler,Pierre van Moerbeke,Pol Vanhaecke

Publisher: Springer Science & Business Media

ISBN: 366205650X

Category: Mathematics

Page: 484

View: 9194

This Ergebnisse volume is aimed at a wide readership of mathematicians and physicists, graduate students and professionals. The main thrust of the book is to show how algebraic geometry, Lie theory and Painlevé analysis can be used to explicitly solve integrable differential equations and construct the algebraic tori on which they linearize; at the same time, it is, for the student, a playing ground to applying algebraic geometry and Lie theory. The book is meant to be reasonably self-contained and presents numerous examples. The latter appear throughout the text to illustrate the ideas, and make up the core of the last part of the book. The first part of the book contains the basic tools from Lie groups, algebraic and differential geometry to understand the main topic.
Posted in Mathematics

Geometry and Dynamics of Integrable Systems

Author: Alexey Bolsinov,Juan J. Morales-Ruiz,Nguyen Tien Zung

Publisher: Birkhäuser

ISBN: 3319335030

Category: Mathematics

Page: 140

View: 4253

Based on lectures given at an advanced course on integrable systems at the Centre de Recerca Matemàtica in Barcelona, these lecture notes address three major aspects of integrable systems: obstructions to integrability from differential Galois theory; the description of singularities of integrable systems on the basis of their relation to bi-Hamiltonian systems; and the generalization of integrable systems to the non-Hamiltonian settings. All three sections were written by top experts in their respective fields. Native to actual problem-solving challenges in mechanics, the topic of integrable systems is currently at the crossroads of several disciplines in pure and applied mathematics, and also has important interactions with physics. The study of integrable systems also actively employs methods from differential geometry. Moreover, it is extremely important in symplectic geometry and Hamiltonian dynamics, and has strong correlations with mathematical physics, Lie theory and algebraic geometry (including mirror symmetry). As such, the book will appeal to experts with a wide range of backgrounds.
Posted in Mathematics

Journal of Physics A

Mathematical and general

Author: N.A

Publisher: N.A

ISBN: N.A

Category: Mathematical physics

Page: N.A

View: 7397

Posted in Mathematical physics

Choice

Publication of the Association of College and Research Libraries, a Division of the American Library Association

Author: N.A

Publisher: N.A

ISBN: N.A

Category: Academic libraries

Page: N.A

View: 3014

Posted in Academic libraries

Journal of Physics

Mathematical and general. A

Author: N.A

Publisher: N.A

ISBN: N.A

Category: Mathematical physics

Page: N.A

View: 2945

Posted in Mathematical physics

Mathematical Reviews

Author: N.A

Publisher: N.A

ISBN: N.A

Category: Mathematics

Page: N.A

View: 6841

Posted in Mathematics

Subject Guide to Books in Print

An Index to the Publishers' Trade List Annual

Author: N.A

Publisher: N.A

ISBN: N.A

Category: American literature

Page: N.A

View: 9531

Posted in American literature

Einführung in die Mechanik und Symmetrie

Eine grundlegende Darstellung klassischer mechanischer Systeme

Author: Jerrold E. Marsden,Tudor S. Ratiu

Publisher: Springer-Verlag

ISBN: 3642568599

Category: Mathematics

Page: 598

View: 524

Symmetrie spielt in der Mechanik eine große Rolle. Dieses Buch beschreibt die Entwicklung zugrunde liegender Theorien. Besonderes Gewicht wird der Symmetrie beigemessen. Ursache hierfür sind Entwicklungen im Bereich dynamischer Systeme, der Einsatz geometrischer Verfahren und neue Anwendungen. Dieses Lehrbuch stellt Grundlagen bereit und beschreibt zahlreiche spezifische Anwendungen. Interessant für Physiker und Ingenieure. Ausgewählte Beispiele, Anwendungen, aktuelle Verfahren/Techniken veranschaulichen die Theorie.
Posted in Mathematics

Books in Print Supplement

Author: N.A

Publisher: N.A

ISBN: N.A

Category: American literature

Page: N.A

View: 9247

Posted in American literature

C. G. J. Jacobi's Vorlesungen Über Dynamik

Gehalten an der Universität zu Königsberg im Wintersemester 1842-1843 und nach Einem von C. W. Borchart Ausgearbeiteten Hefte (Classic Reprint)

Author: Carl Gustav Jakob Jacobi

Publisher: Forgotten Books

ISBN: 9780484314244

Category: Mathematics

Page: 306

View: 4961

Excerpt from C. G. J. Jacobi's Vorlesungen Uber Dynamik: Gehalten an der Universitat zu Konigsberg im Wintersemester 1842-1843 und nach Einem von C. W. Borchart Ausgearbeiteten Hefte Dritte Vorlesung. Das Princip der Erhaltung der Bewegung des Schwerpunkts. Vierte Vorlesung. Das Princip der Erhaltung der lebendigen Kraft. About the Publisher Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.
Posted in Mathematics

Books in Print, 2004-2005

Author: N.A

Publisher: N.A

ISBN: 9780835246477

Category: Literature

Page: N.A

View: 5636

Posted in Literature

Special Relativity

Author: Nicholas M.J. Woodhouse

Publisher: Springer-Verlag

ISBN: 3540466762

Category: Science

Page: 88

View: 1060

Posted in Science

INIS Atomindex

INIS Atomindeks

Author: N.A

Publisher: N.A

ISBN: N.A

Category: Nuclear energy

Page: N.A

View: 6168

Posted in Nuclear energy

Applied Mechanics Reviews

Author: N.A

Publisher: N.A

ISBN: N.A

Category: Mechanics, Applied

Page: N.A

View: 2958

Posted in Mechanics, Applied