Symplectic Geometry of Integrable Hamiltonian Systems

Symplectic Geometry of Integrable Hamiltonian Systems
Title Symplectic Geometry of Integrable Hamiltonian Systems PDF eBook
Author Michèle Audin
Publisher Birkhäuser
Pages 225
Release 2012-12-06
Genre Mathematics
ISBN 3034880715

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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.

Symplectic Geometry, Groupoids, and Integrable Systems

Symplectic Geometry, Groupoids, and Integrable Systems
Title Symplectic Geometry, Groupoids, and Integrable Systems PDF eBook
Author Pierre Dazord
Publisher Springer Science & Business Media
Pages 318
Release 2012-12-06
Genre Mathematics
ISBN 1461397197

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The papers, some of which are in English, the rest in French, in this volume are based on lectures given during the meeting of the Seminare Sud Rhodanien de Geometrie (SSRG) organized at the Mathematical Sciences Research Institute in 1989. The SSRG was established in 1982 by geometers and mathematical physicists with the aim of developing and coordinating research in symplectic geometry and its applications to analysis and mathematical physics. Among the subjects discussed at the meeting, a special role was given to the theory of symplectic groupoids, the subject of fruitful collaboration involving geometers from Berkeley, Lyon, and Montpellier.

Differential Geometry and Integrable Systems

Differential Geometry and Integrable Systems
Title Differential Geometry and Integrable Systems PDF eBook
Author Martin A. Guest
Publisher American Mathematical Soc.
Pages 370
Release 2002
Genre Mathematics
ISBN 0821829386

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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 byintegrable systems. This book is the first of three collections of expository and research articles. This volume focuses on differential geometry. It is remarkable that many classical objects in surface theory and submanifold theory are described as integrable systems. Having such a description generallyreveals previously unnoticed symmetries and can lead to surprisingly explicit solutions. Surfaces of constant curvature in Euclidean space, harmonic maps from surfaces to symmetric spaces, and analogous structures on higher-dimensional manifolds are some of the examples that have broadened the horizons of differential geometry, bringing a rich supply of concrete examples into the theory of integrable systems. Many of the articles in this volume are written by prominent researchers and willserve 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 second volume from this conference also available from the AMS is Integrable Systems,Topology, and Physics, Volume 309 CONM/309in 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.

Lectures on Symplectic Geometry

Lectures on Symplectic Geometry
Title Lectures on Symplectic Geometry PDF eBook
Author Ana Cannas da Silva
Publisher Springer
Pages 240
Release 2004-10-27
Genre Mathematics
ISBN 354045330X

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The goal of these notes is to provide a fast introduction to symplectic geometry for graduate students with some knowledge of differential geometry, de Rham theory and classical Lie groups. This text addresses symplectomorphisms, local forms, contact manifolds, compatible almost complex structures, Kaehler manifolds, hamiltonian mechanics, moment maps, symplectic reduction and symplectic toric manifolds. It contains guided problems, called homework, designed to complement the exposition or extend the reader's understanding. There are by now excellent references on symplectic geometry, a subset of which is in the bibliography of this book. However, the most efficient introduction to a subject is often a short elementary treatment, and these notes attempt to serve that purpose. This text provides a taste of areas of current research and will prepare the reader to explore recent papers and extensive books on symplectic geometry where the pace is much faster. For this reprint numerous corrections and clarifications have been made, and the layout has been improved.

Integrable Hamiltonian Systems

Integrable Hamiltonian Systems
Title Integrable Hamiltonian Systems PDF eBook
Author A.V. Bolsinov
Publisher CRC Press
Pages 752
Release 2004-02-25
Genre Mathematics
ISBN 0203643429

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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,

Differential Geometry and Mathematical Physics

Differential Geometry and Mathematical Physics
Title Differential Geometry and Mathematical Physics PDF eBook
Author Gerd Rudolph
Publisher Springer Science & Business Media
Pages 766
Release 2012-11-09
Genre Science
ISBN 9400753454

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Starting from an undergraduate level, this book systematically develops the basics of • Calculus on manifolds, vector bundles, vector fields and differential forms, • Lie groups and Lie group actions, • Linear symplectic algebra and symplectic geometry, • Hamiltonian systems, symmetries and reduction, integrable systems and Hamilton-Jacobi theory. The topics listed under the first item are relevant for virtually all areas of mathematical physics. The second and third items constitute the link between abstract calculus and the theory of Hamiltonian systems. The last item provides an introduction to various aspects of this theory, including Morse families, the Maslov class and caustics. The book guides the reader from elementary differential geometry to advanced topics in the theory of Hamiltonian systems with the aim of making current research literature accessible. The style is that of a mathematical textbook,with full proofs given in the text or as exercises. The material is illustrated by numerous detailed examples, some of which are taken up several times for demonstrating how the methods evolve and interact.

Symplectic Geometry

Symplectic Geometry
Title Symplectic Geometry PDF eBook
Author A.T. Fomenko
Publisher CRC Press
Pages 488
Release 1995-11-30
Genre Mathematics
ISBN 9782881249013

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