Algebraic Integrability, Painlev� Geometry and Lie Algebras

Algebraic Integrability, Painlev� Geometry and Lie Algebras


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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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Product Details

ISBN-13: 9783540224709
Publisher: Springer Berlin Heidelberg
Publication date: 10/15/2004
Series: Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics , #47
Edition description: 2004
Pages: 484
Product dimensions: 6.10(w) x 9.25(h) x 0.04(d)

Table of Contents

1 Introduction.- 2 Lie Algebras.- 3 Poisson Manifolds.- 4 Integrable Systems on Poisson Manifolds.- 5 The Geometry of Abelian Varieties.- 6 A.c.i. Systems.- 7 Weight Homogeneous A.c.i. Systems.- 8 Integrable Geodesic Flow on SO(4).- 9 Periodic Toda Lattices Associated to Cartan Matrices.- 10 Integrable Spinning Tops.- References.

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