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© 2004

Algebraic Integrability, Painlevé Geometry and Lie Algebras

  • Aimed at a wide readership of mathematicians and physicists, graduate students and professionals

  • The main thrust of the book is to show how algebraic geometry, Lie theory and Painlevé analysis can be used to explicitly solve integrable differential equations and to construct the algebraic tori on which they linearize

  • The book is reasonably self-contained and presents numerous examples

Book

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

Table of contents

  1. Front Matter
    Pages I-XII
  2. Introduction

    1. Mark Adler, Pierre van Moerbeke, Pol Vanhaecke
      Pages 1-4
  3. Liouville Integrable Systems

    1. Front Matter
      Pages 5-5
    2. Mark Adler, Pierre van Moerbeke, Pol Vanhaecke
      Pages 7-39
    3. Mark Adler, Pierre van Moerbeke, Pol Vanhaecke
      Pages 41-66
    4. Mark Adler, Pierre van Moerbeke, Pol Vanhaecke
      Pages 67-104
  4. Algebraic Completely Integrable Systems

    1. Front Matter
      Pages 105-105
    2. Mark Adler, Pierre van Moerbeke, Pol Vanhaecke
      Pages 107-152
    3. Mark Adler, Pierre van Moerbeke, Pol Vanhaecke
      Pages 153-197
    4. Mark Adler, Pierre van Moerbeke, Pol Vanhaecke
      Pages 199-261
  5. Examples

    1. Front Matter
      Pages 263-263
    2. Mark Adler, Pierre van Moerbeke, Pol Vanhaecke
      Pages 265-360
    3. Mark Adler, Pierre van Moerbeke, Pol Vanhaecke
      Pages 361-418
    4. Mark Adler, Pierre van Moerbeke, Pol Vanhaecke
      Pages 419-468
  6. Back Matter
    Pages 469-483

About this book

Keywords

Abelian varieties Lie theory algebra curve theory integrable systems mathematical physics

Authors and affiliations

  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

  • Book Title Algebraic Integrability, Painlevé Geometry and Lie Algebras
  • Authors Mark Adler
    Pierre van Moerbeke
    Pol Vanhaecke
  • Series Title Ergebnisse der Mathematik und ihrer Grenzgebiete
  • 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
  • Hardcover ISBN 978-3-540-22470-9
  • Softcover ISBN 978-3-642-06128-8
  • eBook ISBN 978-3-662-05650-9
  • Series ISSN 0071-1136
  • Edition Number 1
  • Number of Pages XII, 484
  • Number of Illustrations 0 b/w illustrations, 0 illustrations in colour
  • Topics Geometry
    Algebraic Geometry
    Topological Groups, Lie Groups
    Mathematical Methods in Physics
  • Buy this book on publisher's site

Reviews

From the reviews of the first edition:

"The aim of this book is to explain ‘how algebraic geometry, Lie theory and Painlevé analysis can be used to explicitly solve integrable differential equations’. … One of the main advantages of this book is that the authors … succeeded to present the material in a self-contained manner with numerous examples. As a result it can be also used as a reference book for many subjects in mathematics. In summary … a very good book which covers many interesting subjects in modern mathematical physics." (Vladimir Mangazeev, The Australian Mathematical Society Gazette, Vol. 33 (4), 2006)

"This is an extensive volume devoted to the integrability of nonlinear Hamiltonian differential equations. The book is designed as a teaching textbook and aims at a wide readership of mathematicians and physicists, graduate students and professionals. … The book provides many useful tools and techniques in the field of completely integrable systems. It is a valuable source for graduate students and researchers who like to enter the integrability theory or to learn fascinating aspects of integrable geometry of nonlinear differential equations." (Ma Wen-Xiu, Zentralblatt MATH, Vol. 1083, 2006)