Last edited by Mezikree
Tuesday, July 28, 2020 | History

6 edition of Momentum Maps and Hamiltonian Reduction found in the catalog.

Momentum Maps and Hamiltonian Reduction

by Juan-Pablo Ortega

  • 86 Want to read
  • 26 Currently reading

Published by Birkhäuser Boston .
Written in English

    Subjects:
  • Analytic topology,
  • Lie groups,
  • Global analysis (Mathematics),
  • Science,
  • Mathematics,
  • Science/Mathematics,
  • Mathematical Physics,
  • Differential Equations,
  • Mathematics / Group Theory,
  • Applied,
  • Global differential geometry,
  • Hamiltonian systems

  • The Physical Object
    FormatHardcover
    Number of Pages320
    ID Numbers
    Open LibraryOL8074794M
    ISBN 100817643079
    ISBN 109780817643072

      (2) Study the momentum map theory defined by a quasi-symplectic groupoid. In particular, we study the reduction theory and prove that the reduced space is always a symplectic manifold. More generally, we prove that the classical intertwiner space between two Hamiltonian $\Gamma$-spaces is always a symplectic manifold whenever it is a smooth. Our goal in this book is to explore some of the connections between control theory and geometric mechanics; that is, we link control theory with a g- metric view of classical mechanics in both its Lagrangian and Hamiltonian formulations and in particular with the theory of mechanical systems s- ject to motion constraints. This synthesis of topics is appropriate, since there is a particularly.

    Momentum map and reduction. One of the principal ideas of geometric mechanics is reduction, which goes back to Jacobi's elimination of the node in the 3-body problem, but in its modern form is due to K. Meyer () and independently J.E. Marsden and A. Weinstein (), both inspired by the work of Smale (). Symmetry of a Hamiltonian or Lagrangian system gives rise to . 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.

    The use of geometric methods in classical mechanics has proven fruitful, with wide applications in physics and engineering. In this book, Professor Marsden concentrates on these geometric aspects, especially on symmetry techniques. The main points he covers are: the stability of relative equilibria, which is analyzed using the block diagonalization technique; geometric . SYMPLECTIC QUOTIENTS: MOMENT MAPS, SYMPLECTIC REDUCTION AND THE MARSDEN-WEINSTEIN-MEYER THEOREM VICTORIA HOSKINS 1. Construction of group quotients in differential geometry Let Xbe a smooth manifold and Kbe a Lie group; then an action of Kon Xis an action ˙: K X!Xwhich is smooth map of manifolds such that ˙ k: X!Xis a di .


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Momentum Maps and Hamiltonian Reduction by Juan-Pablo Ortega Download PDF EPUB FB2

The exposition reviews the necessary prerequisites, beginning with an introduction to Lie symmetries on Poisson and symplectic manifolds.

This is followed by a discussion of momentum maps and the geometry of conservation laws that are used in. Momentum Maps and Hamiltonian Reduction (Progress in Mathematics) Softcover reprint of the original 1st ed.

Edition by Juan-Pablo Ortega (Author) › Visit Amazon's Juan-Pablo Ortega Page. Find all the books, read about the author, and more. Format: Paperback. from book Momentum Maps and Hamiltonian Reduction (pp) Momentum Maps and Hamiltonian Reduction.

The statement above shows that this remains true for cylinder valued momentum maps, where. from book Momentum Maps and Hamiltonian Reduction (pp) Momentum Maps and Hamiltonian Reduction.

Momentum Maps and Hamiltonian Reduction book January Momentum Maps and Hamiltonian Reduction. Authors: Ortega, Juan-Pablo, This is followed by a discussion of momentum maps and the geometry of conservation laws that are used in the development of symplectic reduction.

and covers a large part of the recent developments related to momentum maps and reduction. This book fills a need and.

Momentum Maps and Hamiltonian Reduction is a great book. This book is written by author Ortega, J. Pablo, Ratiu, Tudor S.

You can read the Momentum Maps and Hamiltonian Reduction book on our website in any convenient format. Momentum maps and Hamiltonian reduction.

Progress in Mathematics. Birkhauser Boston. ISBN Audin, Michèle (), Torus actions on symplectic manifolds, Progress in Mathematics, 93 (Second revised ed.), Birkhäuser, ISBN The Momentum Map, Symplectic Reduction and an Introduction to Brownian Motion Master’s Thesis, Fall Semester Mechanics.

The rst part is a presentation of symplectic reduction, going through the momentum map and culminating with an explicit Momentum maps as a generalization of hamiltonian functions Momentum maps hamiltonian reduction pdf Murcia, September Momentum Maps and Hamiltonian Reduction.

Digitally watermarked, mg zr sales brochure pdf no DRM included format: PDF eBooks can be used on all Reading Devices first part is a presentation of symplectic reduction, going through the.

momentum maps and hamiltonian reduction. Lie group valued momentum maps The optimal momentum map Momentum maps and groupoid moment maps 6 Regular Symplectic Reduction Theory Point reduction Coadjoint orbits as point reduced spaces Orbit reduction The regular reduction diagram Reduction by shift Compra Momentum Maps and Hamiltonian Reduction.

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Tutte le categorie. VAI Author: Juan-Pablo Ortega. Remark (Uniqueness of momentum maps). If and are two momentum maps for the same action, then for all X2g, d(X X) = 0: Because Mis supposed to be connected, this implies that the di erence X X is a constant function, say c X, on M.

By de nition of momentum maps, the constant c X depends linearly on X. So there is a an element ˘2g such that File Size: KB. Momentum Maps and Hamiltonian Reduction 在线试读 * Winner of the Ferran Sunyer i Balaguer Prize in * Reviews the necessary prerequisites, beginning with an introduction to Lie symmetries on Poisson and symplectic manifolds.*.

Get this from a library. Momentum maps and Hamiltonian reduction. [Juan-Pablo Ortega; Tudor S Rațiu] -- "The focus of this work is a comprehensive and self-contained presentation of the intimate connection between symmetries, conservation laws, and reduction, treating the singular case in detail.".

Momentum maps and Hamiltonian reduction. [Juan-Pablo Ortega; Tudor S Ratiu] smooth structures * Lie group actions * Pseudogroups and groupoids * The standard momentum map * Generalizations of the momentum map * Regular symplectic reduction theory * The Symplectic Slice Theorem * Singular reduction and the stratification theorem * Optimal.

Momentum Maps and Hamiltonian Reduction 作者: Juan-Pablo Ortega / Tudor S. Ratiu 出版社: Birkhäuser Boston 出版年: 页数: 定价: USD 装帧: Hardcover 丛书: Progress in Mathematics.

Momentum Maps and Hamiltonian Reduction by Juan-Pablo Ortega; Tudor S. Ratiu. Birkhäuser Boston, Hardcover. Good. Momentum maps and reduction in algebraic geometp [ for natural examples of nonequivariant momentum maps).

That is, we shall assume that I_L: X + k* is K-equivariant with respect to the given action of K on X and the coadjoint action of K on k*.

Momentum Maps In this chapter we show how to obtain conserved quantities for Lagrangian and Hamiltonian systems with symmetries. This is done using the con-cept of a momentum mapping, which is a geometric generalization of the classical linear and angular momentum. This concept is more than a math.

Momentum maps and reduction in algebraic geometry This result reduces the problem of rinding a formula for i]o[i^~1 (0)/K] in terms of data on X localised near X7 to the case when K = T is itself a torus.

Guillemin and Kalkman, and independently Martin, then Cited by:. Abstract. In this chapter we use the optimal momentum map introduced in Chapter 5 to carry out symplectic reduction. The reduced spaces that we will obtain generalize the symplectic strata presented in Chapter 8 to the categories in which the optimal momentum map is well defined.Momentum Maps, Dual Pairs and Reduction in Deformation Quantization∗ Henrique Bursztyn January, Abstract This paper is a brief survey of momentum maps, dual pairs and reduction in deforma-tion quantization.

We recall the classical theory of momentum maps in Poisson geometry and present its quantum counterpart.Poisson geometry, Hamiltonian systems, Lie algebras and Lie groups actions on symplectic or Poisson manifolds, momentum maps and their use for the reduction of Hamiltonian systems.

It should be accessible to readers with a general knowledge of basic notions in differential geometry. Full proofs of many results are provided. CONTENTS 1.