Symplectic Reduction By Stages PDF Download
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Author | : Jerrold E. Marsden |
Publisher | : Springer |
Total Pages | : 527 |
Release | : 2007-06-05 |
Genre | : Mathematics |
ISBN | : 3540724702 |
Download Hamiltonian Reduction by Stages Book in PDF, ePub and Kindle
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 | : Matthew Perlmutter |
Publisher | : |
Total Pages | : 274 |
Release | : 1999 |
Genre | : |
ISBN | : |
Download Symplectic Reduction by Stages Book in PDF, ePub and Kindle
Author | : Jerrold E. Marsden |
Publisher | : |
Total Pages | : 0 |
Release | : 2007 |
Genre | : Differentiable dynamical systems |
ISBN | : 9788354072478 |
Download Hamiltonian Reduction by Stages Book in PDF, ePub and Kindle
In this volume readers will find for the first time a detailed account of the theory of symplectic reduction by stages, along with numerous illustrations of the theory. Special emphasis is given to group extensions, including a detailed discussion of the Euclidean group, the oscillator group, the Bott-Virasoro group and other groups of matrices. Ample background theory on symplectic reduction and cotangent bundle reduction in particular is provided. Novel features of the book are the inclusion of a systematic treatment of the cotangent bundle case, including the identification of cocycles with magnetic terms, as well as the general theory of singular reduction by stages.
Author | : Ana Cannas da Silva |
Publisher | : Springer |
Total Pages | : 240 |
Release | : 2004-10-27 |
Genre | : Mathematics |
ISBN | : 354045330X |
Download Lectures on Symplectic Geometry Book in PDF, ePub and Kindle
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 | : Juan-Pablo Ortega |
Publisher | : Springer Science & Business Media |
Total Pages | : 526 |
Release | : 2013-04-17 |
Genre | : Mathematics |
ISBN | : 1475738110 |
Download Momentum Maps and Hamiltonian Reduction Book in PDF, ePub and Kindle
* 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 | : Hernán Cendra |
Publisher | : American Mathematical Soc. |
Total Pages | : 125 |
Release | : 2001 |
Genre | : Mathematics |
ISBN | : 0821827154 |
Download Lagrangian Reduction by Stages Book in PDF, ePub and Kindle
This booklet studies the geometry of the reduction of Lagrangian systems with symmetry in a way that allows the reduction process to be repeated; that is, it develops a context for Lagrangian reduction by stages. The Lagrangian reduction procedure focuses on the geometry of variational structures and how to reduce them to quotient spaces under group actions. This philosophy is well known for the classical cases, such as Routh reduction for systems with cyclic variables (where the symmetry group is Abelian) and Euler-Poincare reduction (for the case in which the configuration space is a Lie group) as well as Euler-Poincare reduction for semidirect products.
Author | : Sebastian Walcher |
Publisher | : World Scientific |
Total Pages | : 306 |
Release | : 2003-01-14 |
Genre | : Science |
ISBN | : 9814486949 |
Download Symmetry And Perturbation Theory - Proceedings Of The International Conference On Spt 2002 Book in PDF, ePub and Kindle
This is the fourth conference on “Supersymmetry and Perturbation Theory” (SPT 2002). The proceedings present original results and state-of-the-art reviews on topics related to symmetry, integrability and perturbation theory, etc.
Author | : Simonetta Abenda |
Publisher | : World Scientific |
Total Pages | : 306 |
Release | : 2002 |
Genre | : Mathematics |
ISBN | : 9812795405 |
Download Symmetry and Perturbation Theory Book in PDF, ePub and Kindle
This is the fourth conference on OC Supersymmetry and Perturbation TheoryOCO (SPT 2002). The proceedings present original results and state-of-the-art reviews on topics related to symmetry, integrability and perturbation theory, etc. Contents: An Outline of the Geometrical Theory of the Separation of Variables in the Hamilton-Jacobi and SchrAdinger Equations (S Benenti); Partial Symmetries and Symmetric Sets of Solutions to PDE's (G Cicogna); On the Algebro-Geometric Solution of 3 x 3 Matrix Riemann-Hilbert Problem (V Enolski & T Grava); Bifurcations in Flow-Induced Vibration (S Fatimah & F Verhulst); Steklov-Lyapunov Type Systems (Yu N Fedorov); Renormalization Group and Summation of Divergent Series for Hyperbolic Invariant Tori (G Gentile); On the Linearization of Holomorphic Vector Fields in the Siegel Domain with Linear Parts Having Nontrivial Jordan Blocks (T Gramchev); Smooth Normalization of a Vector Field Near an Invariant Manifold (A Kopanskii); Inverse Problems for SL (2) Lattices (V B Kuznetsov); Some Remarks about the Geometry of Hamiltonian Conservation Laws (J-P Ortega); Janet's Algorithm (W Plesken); Some Integrable Billiards (E Previato); Symmetries of Relative Equilibria for Simple Mechanical Systems (M Rodr guez-Olmos & M E Sousa Dias); A Spectral Sequences Approach to Normal Forms (J A Sanders); Rational Parametrization of Strata in Orbit Spaces of Compact Linear Groups (G Sartori & G Valente); Effective Hamiltonians and Perturbation Theory for Quantum Bound States of Nuclear Motion in Molecules (V G Tyuterev); Generalized Hasimoto Transformation and Vector Sine-Gordon Equation (J P Wang); and other papers. Readership: Researchers and graduate students in mathematical and theoretical physics, and nonlinear science."
Author | : Shubham Dwivedi |
Publisher | : Springer Nature |
Total Pages | : 132 |
Release | : 2019-09-23 |
Genre | : Mathematics |
ISBN | : 3030272273 |
Download Hamiltonian Group Actions and Equivariant Cohomology Book in PDF, ePub and Kindle
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.
Author | : A. G. Khovanskiĭ |
Publisher | : American Mathematical Soc. |
Total Pages | : 242 |
Release | : 1998 |
Genre | : Mathematics |
ISBN | : 9780821810941 |
Download Geometry of Differential Equations Book in PDF, ePub and Kindle
This volume contains articles written by V. I. Arnold's colleagues on the occasion of his 60th birthday. The articles are mostly devoted to various aspects of geometry of differential equations and relations to global analysis and Hamiltonian mechanics.