Momentum Maps And Hamiltonian Reduction

Author : Juan-Pablo Ortega
Publisher : Springer Science & Business Media
ISBN 13 : 1475738110
Total Pages : 526 pages
Book Rating : 4.17/5 ( download)

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Download or read book Momentum Maps and Hamiltonian Reduction written by Juan-Pablo Ortega and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 526 pages. Available in PDF, EPUB and Kindle. Book excerpt: * 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.

Author : Juan Pablo Ortega
Publisher :
ISBN 13 : 9781475738124
Total Pages : 536 pages
Book Rating : 4.29/5 ( download)

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Download or read book Momentum Maps and Hamiltonian Reduction written by Juan Pablo Ortega and published by . This book was released on 2014-01-15 with total page 536 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author : Jerrold E. Marsden
Publisher : Springer
ISBN 13 : 3540724702
Total Pages : 524 pages
Book Rating : 4.04/5 ( download)

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Download or read book Hamiltonian Reduction by Stages written by Jerrold E. Marsden and published by Springer. This book was released on 2007-06-05 with total page 524 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Author : Pierre Dazord
Publisher : Springer Science & Business Media
ISBN 13 : 1461397197
Total Pages : 318 pages
Book Rating : 4.99/5 ( download)

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Download or read book Symplectic Geometry, Groupoids, and Integrable Systems written by Pierre Dazord and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 318 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Author : Victor Guillemin
Publisher : American Mathematical Soc.
ISBN 13 : 0821805029
Total Pages : 362 pages
Book Rating : 4.22/5 ( download)

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Download or read book Moment Maps, Cobordisms, and Hamiltonian Group Actions written by Victor Guillemin and published by American Mathematical Soc.. This book was released on 2002 with total page 362 pages. Available in PDF, EPUB and Kindle. Book excerpt: During the last 20 years, ``localization'' has been one of the dominant themes in the area of equivariant differential geometry. Typical results are the Duistermaat-Heckman theory, the Berline-Vergne-Atiyah-Bott localization theorem in equivariant de Rham theory, and the ``quantization commutes with reduction'' theorem and its various corollaries. To formulate the idea that these theorems are all consequences of a single result involving equivariant cobordisms, the authors have developed a cobordism theory that allows the objects to be non-compact manifolds. A key ingredient in this non-compact cobordism is an equivariant-geometrical object which they call an ``abstract moment map''. This is a natural and important generalization of the notion of a moment map occurring in the theory of Hamiltonian dynamics. The book contains a number of appendices that include introductions to proper group-actions on manifolds, equivariant cohomology, Spin${^\mathrm{c}}$-structures, and stable complex structures. It is geared toward graduate students and research mathematicians interested in differential geometry. It is also suitable for topologists, Lie theorists, combinatorists, and theoretical physicists. Prerequisite is some expertise in calculus on manifolds and basic graduate-level differential geometry.

Author : Jerrold E. Marsden
Publisher : Springer Science & Business Media
ISBN 13 : 0817644199
Total Pages : 666 pages
Book Rating : 4.92/5 ( download)

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Download or read book The Breadth of Symplectic and Poisson Geometry written by Jerrold E. Marsden and published by Springer Science & Business Media. This book was released on 2007-07-03 with total page 666 pages. Available in PDF, EPUB and Kindle. Book excerpt: * 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

Author : Ana Cannas da Silva
Publisher : Springer
ISBN 13 : 354045330X
Total Pages : 220 pages
Book Rating : 4.07/5 ( download)

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Download or read book Lectures on Symplectic Geometry written by Ana Cannas da Silva and published by Springer. This book was released on 2004-10-27 with total page 220 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Author : Holm Darryl D
Publisher : World Scientific Publishing Company
ISBN 13 : 1911298658
Total Pages : 468 pages
Book Rating : 4.56/5 ( download)

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Download or read book Geometric Mechanics - Part I: Dynamics And Symmetry (2nd Edition) written by Holm Darryl D and published by World Scientific Publishing Company. This book was released on 2011-07-13 with total page 468 pages. Available in PDF, EPUB and Kindle. Book excerpt: See also GEOMETRIC MECHANICS — Part II: Rotating, Translating and Rolling (2nd Edition) This textbook introduces the tools and language of modern geometric mechanics to advanced undergraduates and beginning graduate students in mathematics, physics and engineering. It treats the fundamental problems of dynamical systems from the viewpoint of Lie group symmetry in variational principles. The only prerequisites are linear algebra, calculus and some familiarity with Hamilton's principle and canonical Poisson brackets in classical mechanics at the beginning undergraduate level.The ideas and concepts of geometric mechanics are explained in the context of explicit examples. Through these examples, the student develops skills in performing computational manipulations, starting from Fermat's principle, working through the theory of differential forms on manifolds and transferring these ideas to the applications of reduction by symmetry to reveal Lie-Poisson Hamiltonian formulations and momentum maps in physical applications.The many Exercises and Worked Answers in the text enable the student to grasp the essential aspects of the subject. In addition, the modern language and application of differential forms is explained in the context of geometric mechanics, so that the importance of Lie derivatives and their flows is clear. All theorems are stated and proved explicitly.The organisation of the first edition has been preserved in the second edition. However, the substance of the text has been rewritten throughout to improve the flow and to enrich the development of the material. In particular, the role of Noether's theorem about the implications of Lie group symmetries for conservation laws of dynamical systems has been emphasised throughout, with many applications./a

Author : Darryl D. Holm
Publisher : Oxford University Press
ISBN 13 : 0191549878
Total Pages : pages
Book Rating : 4.78/5 ( download)

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Download or read book Geometric Mechanics and Symmetry written by Darryl D. Holm and published by Oxford University Press. This book was released on 2009-07-30 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Classical mechanics, one of the oldest branches of science, has undergone a long evolution, developing hand in hand with many areas of mathematics, including calculus, differential geometry, and the theory of Lie groups and Lie algebras. The modern formulations of Lagrangian and Hamiltonian mechanics, in the coordinate-free language of differential geometry, are elegant and general. They provide a unifying framework for many seemingly disparate physical systems, such as n particle systems, rigid bodies, fluids and other continua, and electromagnetic and quantum systems. Geometric Mechanics and Symmetry is a friendly and fast-paced introduction to the geometric approach to classical mechanics, suitable for a one- or two- semester course for beginning graduate students or advanced undergraduates. It fills a gap between traditional classical mechanics texts and advanced modern mathematical treatments of the subject. After a summary of the necessary elements of calculus on smooth manifolds and basic Lie group theory, the main body of the text considers how symmetry reduction of Hamilton's principle allows one to derive and analyze the Euler-Poincaré equations for dynamics on Lie groups. Additional topics deal with rigid and pseudo-rigid bodies, the heavy top, shallow water waves, geophysical fluid dynamics and computational anatomy. The text ends with a discussion of the semidirect-product Euler-Poincaré reduction theorem for ideal fluid dynamics. A variety of examples and figures illustrate the material, while the many exercises, both solved and unsolved, make the book a valuable class text.

Author : Shubham Dwivedi
Publisher : Springer Nature
ISBN 13 : 3030272273
Total Pages : 132 pages
Book Rating : 4.72/5 ( download)

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Download or read book Hamiltonian Group Actions and Equivariant Cohomology written by Shubham Dwivedi and published by Springer Nature. This book was released on 2019-09-23 with total page 132 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph could be used for a graduate course on symplectic geometry as well as for independent study. The monograph starts with an introduction of symplectic vector spaces, followed by symplectic manifolds and then Hamiltonian group actions and the Darboux theorem. After discussing moment maps and orbits of the coadjoint action, symplectic quotients are studied. The convexity theorem and toric manifolds come next and we give a comprehensive treatment of Equivariant cohomology. The monograph also contains detailed treatment of the Duistermaat-Heckman Theorem, geometric quantization, and flat connections on 2-manifolds. Finally, there is an appendix which provides background material on Lie groups. A course on differential topology is an essential prerequisite for this course. Some of the later material will be more accessible to readers who have had a basic course on algebraic topology. For some of the later chapters, it would be helpful to have some background on representation theory and complex geometry.