A.c.i. Systems

  • Mark Adler
  • Pierre van Moerbeke
  • Pol Vanhaecke
Chapter
Part of the Ergebnisse der Mathematik und ihrer Grenzgebiete book series (MATHE3, volume 47)

Abstract

Many integrable systems from classical mechanics admit a complexification, where phase space and time are complexified, and the geometry of the (complex) momentum map is the best possible complex analogue of the geometry that appears in the Liouville Theorem (Theorem 4.28). Namely, in many relevant examples the generic complexified fiber is an affine part of an Abelian variety (a compact algebraic torus, see Chapter 5) and the integrable vector fields are translation invariant, when restricted to any of these tori. Such integrable systems are the main topic of this book, and we will call them algebraic completely integrable systems, following the original definition of Adler and van Moerbeke (see [14]).

Keywords

Manifold Lution Dinate Grinding Fami 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Copyright information

© Springer-Verlag Berlin Heidelberg 2004

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

Personalised recommendations