Hamiltonian Reduction by Stages

  • Jerrold E. Marsden
  • Gerard Misiolek
  • Juan-Pablo Ortega
  • Matthew Perlmutter
  • Tudor S. Ratiu

Part of the Lecture Notes in Mathematics book series (LNM, volume 1913)

Table of contents

  1. Front Matter
    Pages I-XV
  2. Background and the Problem Setting

    1. Front Matter
      Pages 1-1
    2. Pages 101-109
  3. Regular Symplectic Reduction by Stages

  4. Optimal Reduction and Singular Reduction by Stages, by Juan-Pablo Ortega

    1. Front Matter
      Pages 421-422
    2. Pages 437-459
  5. Back Matter
    Pages 483-523

About this book

Introduction

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.

Keywords

DEX Hamiltonian Volume distribution group identification matrices mechanics momentum reduction symmetry symplectic time

Authors and affiliations

  • Jerrold E. Marsden
    • 1
  • Gerard Misiolek
    • 2
  • Juan-Pablo Ortega
    • 3
  • Matthew Perlmutter
    • 4
  • Tudor S. Ratiu
    • 5
  1. 1.California Institute of TechnologyPasadenaUSA
  2. 2.Department of MathematicsUniversity of Notre DameNotre DameUSA
  3. 3.Département de Mathématiques de BesançonUniversité de Franche-Comté UFR des Sciences et TechniquesF-25030Besançon cedexFrance
  4. 4.Institute of Fundamental SciencesMassey UniversityPalmerston NorthNew Zealand
  5. 5.Section de MathématiquesEcole Polytechnique Fédérale de LausanneLausanneSwitzerland

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-540-72470-4
  • Copyright Information Springer-Verlag Berlin Heidelberg 2007
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-540-72469-8
  • Online ISBN 978-3-540-72470-4
  • Series Print ISSN 0075-8434
  • Series Online ISSN 1617-9692
  • About this book