Algebraic Integrability, Painlevé Geometry and Lie Algebras

  • Mark Adler
  • Pierre van Moerbeke
  • Pol Vanhaecke
Book

Part of the Ergebnisse der Mathematik und ihrer Grenzgebiete book series (MATHE3, volume 47)

Table of contents

  1. Front Matter
    Pages I-XII
    PDF

  2. Introduction

    1. Introduction
      Mark Adler, Pierre van Moerbeke, Pol Vanhaecke
      Pages 1-4

  3. Liouville Integrable Systems

    1. Front Matter
      Pages 5-5
      PDF
    2. Lie Algebras
      Mark Adler, Pierre van Moerbeke, Pol Vanhaecke
      Pages 7-39
    3. Poisson Manifolds
      Mark Adler, Pierre van Moerbeke, Pol Vanhaecke
      Pages 41-66
    4. Integrable Systems on Poisson Manifolds
      Mark Adler, Pierre van Moerbeke, Pol Vanhaecke
      Pages 67-104

  4. Algebraic Completely Integrable Systems

    1. Front Matter
      Pages 105-105
      PDF
    2. The Geometry of Abelian Varieties
      Mark Adler, Pierre van Moerbeke, Pol Vanhaecke
      Pages 107-152
    3. A.c.i. Systems
      Mark Adler, Pierre van Moerbeke, Pol Vanhaecke
      Pages 153-197
    4. Weight Homogeneous A.c.i. Systems
      Mark Adler, Pierre van Moerbeke, Pol Vanhaecke
      Pages 199-261

  5. Examples

    1. Front Matter
      Pages 263-263
      PDF
    2. Integrable Geodesic Flow on SO(4)
      Mark Adler, Pierre van Moerbeke, Pol Vanhaecke
      Pages 265-360
    3. Periodic Toda Lattices Associated to Cartan Matrices
      Mark Adler, Pierre van Moerbeke, Pol Vanhaecke
      Pages 361-418
    4. Integrable Spinning Tops
      Mark Adler, Pierre van Moerbeke, Pol Vanhaecke
      Pages 419-468
  6. Back Matter
    Pages 469-483
    PDF

About this book

Keywords

Abelian varieties Lie theory algebra curve theory integrable systems mathematical physics

Authors and affiliations

  • Mark Adler
    • 1
  • Pierre van Moerbeke
    • 1
    • 2
  • Pol Vanhaecke
    • 3
  1. 1.Department of MathematicsBrandeis UniversityWalthamUSA
  2. 2.Department of MathematicsUniversity of LouvainLouvain-la-NeuveBelgium
  3. 3.Laboratoire de Mathématiques et ApplicationsUniversité de PoitiersFuturoscopeFrance

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-662-05650-9
  • Copyright Information Springer-Verlag Berlin Heidelberg 2004
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-642-06128-8
  • Online ISBN 978-3-662-05650-9
  • Series Print ISSN 0071-1136
  • Buy this book on publisher's site