Symplectic Geometry Of Integrable Hamiltonian Systems
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Symplectic Geometry Of Integrable Hamiltonian Systems
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Author : Michèle Audin
language : en
Publisher: Springer Science & Business Media
Release Date : 2003-04-24
Symplectic Geometry Of Integrable Hamiltonian Systems written by Michèle Audin and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-04-24 with Mathematics categories.
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
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Author : Pierre Dazord
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Symplectic Geometry Groupoids And Integrable Systems written by Pierre Dazord and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
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.
Lectures On Symplectic Geometry
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Author : Ana Cannas da Silva
language : en
Publisher: Springer
Release Date : 2004-10-27
Lectures On Symplectic Geometry written by Ana Cannas da Silva and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-10-27 with Mathematics categories.
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.
Differential Geometry And Mathematical Physics
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Author : Gerd Rudolph
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-11-09
Differential Geometry And Mathematical Physics written by Gerd Rudolph and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-11-09 with Science categories.
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.
Integrable Hamiltonian Systems
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Author : A.V. Bolsinov
language : en
Publisher: CRC Press
Release Date : 2004-02-25
Integrable Hamiltonian Systems written by A.V. Bolsinov and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-02-25 with Mathematics categories.
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,
Hamiltonian Systems And Their Integrability
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Author : Mich'le Audin
language : en
Publisher: American Mathematical Soc.
Release Date : 2008
Hamiltonian Systems And Their Integrability written by Mich'le Audin and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008 with Mathematics categories.
Hamiltonian systems began as a mathematical approach to the study of mechanical systems. As the theory developed, it became clear that the systems that had a sufficient number of conserved quantities enjoyed certain remarkable properties. These are the completely integrable systems. In time, a rich interplay arose between integrable systems and other areas of mathematics, particularly topology, geometry, and group theory.This book presents some modern techniques in the theory of integrable systems viewed as variations on the theme of action-angle coordinates. These techniques include analytical methods coming from the Galois theory of differential equations, as well as more classical algebro-geometric methods related to Lax equations. Audin has included many examples and exercises. Most of the exercises build on the material in the text. None of the important proofs have been relegated to the exercises. Many of the examples are classical, rather than abstract. This book would be suitable for a graduate course in Hamiltonian systems.
Dynamical Systems Iv
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Author : V.I. Arnol'd
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-06-29
Dynamical Systems Iv written by V.I. Arnol'd and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-06-29 with Mathematics categories.
This book takes a snapshot of the mathematical foundations of classical and quantum mechanics from a contemporary mathematical viewpoint. It covers a number of important recent developments in dynamical systems and mathematical physics and places them in the framework of the more classical approaches; the presentation is enhanced by many illustrative examples concerning topics which have been of especial interest to workers in the field, and by sketches of the proofs of the major results. The comprehensive bibliographies are designed to permit the interested reader to retrace the major stages in the development of the field if he wishes. Not so much a detailed textbook for plodding students, this volume, like the others in the series, is intended to lead researchers in other fields and advanced students quickly to an understanding of the 'state of the art' in this area of mathematics. As such it will serve both as a basic reference work on important areas of mathematical physics as they stand today, and as a good starting point for further, more detailed study for people new to this field.
Symplectic Geometry
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Author : A.T. Fomenko
language : en
Publisher: CRC Press
Release Date : 1995-11-30
Symplectic Geometry written by A.T. Fomenko and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995-11-30 with Mathematics categories.
Symplectic Geometry And Analytical Mechanics
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Author : P. Libermann
language : en
Publisher: Springer Science & Business Media
Release Date : 1987-03-31
Symplectic Geometry And Analytical Mechanics written by P. Libermann and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 1987-03-31 with Mathematics categories.
Approach your problems from the right end It isn't that they can't see the solution. and begin with the answers. Then one day, It is that they can't see the problem. perhaps you will find the final question. G. K. Chesterton. The Scandal of Father 'The Hermit Clad in Crane Feathers' Brown 'The point of a Pin'. in R. van Gulik's The Chinese Maze Murders. Growing specialization and diversification have brought a host of monographs and textbooks on increasingly specialized topics. However, the "tree" of knowledge of mathematics and related fields does not grow only by putting forth new branches. It also happens, quite often in fact, that branches which were thouglit to be completely disparate are suddenly seen to be related. Further, the kind and level of sophistication of mathematics applied in various sci ences has changed drastically in recent years: measure theory is used (non-trivially) in re gional and theoretical economics; algebraic geometry interacts with physics; the Minkowsky lemma, coding theory and the structure of water meet one another in packing and covering theory; quantum fields, crystal defects and mathematical programming profit from homo topy theory; Lie algebras are relevant to filtering; and prediction and electrical engineering can use Stein spaces.
Integrable Hamiltonian Hierarchies
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Author : Vladimir Gerdjikov
language : en
Publisher: Springer
Release Date : 2008-12-02
Integrable Hamiltonian Hierarchies written by Vladimir Gerdjikov and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-12-02 with Science categories.
This book presents a detailed derivation of the spectral properties of the Recursion Operators allowing one to derive all the fundamental properties of the soliton equations and to study their hierarchies.