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]).
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2004 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Adler, M., van Moerbeke, P., Vanhaecke, P. (2004). A.c.i. Systems. In: Algebraic Integrability, Painlevé Geometry and Lie Algebras. Ergebnisse der Mathematik und ihrer Grenzgebiete, vol 47. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-05650-9_6
Download citation
DOI: https://doi.org/10.1007/978-3-662-05650-9_6
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-06128-8
Online ISBN: 978-3-662-05650-9
eBook Packages: Springer Book Archive