Momentum Maps and Hamiltonian Reduction

Momentum Maps and Hamiltonian Reduction
Author: Juan-Pablo Ortega
Publisher: Springer Science & Business Media
Total Pages: 526
Release: 2013-04-17
Genre: Mathematics
ISBN: 1475738110

* Winner of the Ferran Sunyer i Balaguer Prize in 2000. * Reviews the necessary prerequisites, beginning with an introduction to Lie symmetries on Poisson and symplectic manifolds. * Currently in classroom use in Europe. * Can serve as a resource for graduate courses and seminars in Hamiltonian mechanics and symmetry, symplectic and Poisson geometry, Lie theory, mathematical physics, and as a comprehensive reference resource for researchers.

Hamiltonian Reduction by Stages

Hamiltonian Reduction by Stages
Author: Jerrold E. Marsden
Publisher: Springer
Total Pages: 527
Release: 2007-06-05
Genre: Mathematics
ISBN: 3540724702

This volume provides a detailed account of the theory of symplectic reduction by stages, along with numerous illustrations of the theory. It gives special emphasis to group extensions, including a detailed discussion of the Euclidean group, the oscillator group, the Bott-Virasoro group and other groups of matrices. The volume also provides ample background theory on symplectic reduction and cotangent bundle reduction.

Symplectic Geometry, Groupoids, and Integrable Systems

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

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.

Symplectic Geometry and Topology

Symplectic Geometry and Topology
Author: Yakov Eliashberg
Publisher: American Mathematical Soc.
Total Pages: 452
Release: 2004
Genre: Mathematics
ISBN: 9780821886892

Symplectic geometry has its origins as a geometric language for classical mechanics. But it has recently exploded into an independent field interconnected with many other areas of mathematics and physics. The goal of the IAS/Park City Mathematics Institute Graduate Summer School on Symplectic Geometry and Topology was to give an intensive introduction to these exciting areas of current research. Included in this proceedings are lecture notes from the following courses: Introductionto Symplectic Topology by D. McDuff; Holomorphic Curves and Dynamics in Dimension Three by H. Hofer; An Introduction to the Seiberg-Witten Equations on Symplectic Manifolds by C. Taubes; Lectures on Floer Homology by D. Salamon; A Tutorial on Quantum Cohomology by A. Givental; Euler Characteristicsand Lagrangian Intersections by R. MacPherson; Hamiltonian Group Actions and Symplectic Reduction by L. Jeffrey; and Mechanics: Symmetry and Dynamics by J. Marsden. Information for our distributors: Titles in this series are copublished with the Institute for Advanced Study/Park City Mathematics Institute. Members of the Mathematical Association of America (MAA) and the National Council of Teachers of Mathematics (NCTM) receive a 20% discount from list price.

The Breadth of Symplectic and Poisson Geometry

The Breadth of Symplectic and Poisson Geometry
Author: Jerrold E. Marsden
Publisher: Springer Science & Business Media
Total Pages: 666
Release: 2007-07-03
Genre: Mathematics
ISBN: 0817644199

* The invited papers in this volume are written in honor of Alan Weinstein, one of the world’s foremost geometers * Contributions cover a broad range of topics in symplectic and differential geometry, Lie theory, mechanics, and related fields * Intended for graduate students and working mathematicians, this text is a distillation of prominent research and an indication of future trends in geometry, mechanics, and mathematical physics

Symplectic Geometry and Analytical Mechanics

Symplectic Geometry and Analytical Mechanics
Author: P. Libermann
Publisher: Springer Science & Business Media
Total Pages: 541
Release: 2012-12-06
Genre: Mathematics
ISBN: 9400938071

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.

Lectures on Symplectic Geometry

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

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

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

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.

Lectures on Mechanics

Lectures on Mechanics
Author: Jerrold E. Marsden
Publisher: Cambridge University Press
Total Pages: 272
Release: 1992-04-30
Genre: Mathematics
ISBN: 9780521428446

Based on the 1991 LMS Invited Lectures given by Professor Marsden, this book discusses and applies symmetry methods to such areas as bifurcations and chaos in mechanical systems.