Algebraic Integrability, Painlevé Geometry and Lie Algebras
By: by Mark Adler, Pierre Moerbeke, Pol Vanhaecke
Contributors: Moerbeke, Pierre; Vanhaecke, Pol
Series: Ergebnisse der Mathematik und ihrer Grenzgebiete, 3. Folge. A Series of Modern Surveys in Mathematics -- 47; Ergebnisse der Mathematik und ihrer Grenzgebiete, 3. Folge. A Series of Modern Surveys in Mathematics -- 47
Publisher: Springer Berlin Heidelberg
Published: 2004
Place of publication: Berlin, Heidelberg
Language: eng
Format: [electronic resource] /
Number of pages: 483
ISBN-13: 9783642061288; 9783662056509
Subjects: Geometry; Mathematics; Mathematical physics; Topological Groups; Geometry, algebraic
Description: This Ergebnisse volume is 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 construct the algebraic tori on which they linearize; at the same time, it is, for the student, a playing ground to applying algebraic geometry and Lie theory. The book is meant to be reasonably self-contained and presents numerous examples. The latter appear throughout the text to illustrate the ideas, and make up the core of the last part of the book. The first part of the book contains the basic tools from Lie groups, algebraic and differential geometry to understand the main topic.
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Table of contents: title: Introduction; title: Part I: Liouville Integrable Systems; Lie Algebras; Poisson Manifolds; Integrable Systems on Poisson Manifolds; title: Part II: Algebraic Completely Integrable Systems; The Geometry of Abelian Varieties; A.c.i. Systems; Weight Homogeneous A.c.i. Systems; title: Part III: Examples; Integrable Geodesic Flow on SO(4); Periodic Toda Lattices Associated to Cartan Matrices; Integrable Spinning Tops; title: References; title: Index.