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Algebraic Integrability, Painlevé Geometry and Lie Algebras

Author: Mark Adler; Pierre Moerbeke; Pol Vanhaecke
Publisher: Berlin, Heidelberg : Springer Berlin Heidelberg, 2004.
Series: Ergebnisse der Mathematik und ihrer Grenzgebiete, 3. Folge. A Series of Modern Surveys in Mathematics, 47.
Edition/Format:   eBook : Document : EnglishView all editions and formats
Database:WorldCat
Summary:
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  Read more...
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Genre/Form: Electronic books
Additional Physical Format: Print version:
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: Mark Adler; Pierre Moerbeke; Pol Vanhaecke
ISBN: 9783662056509 366205650X
OCLC Number: 851367091
Description: 1 online resource (xii, 483 pages).
Contents: Introduction --
Part I: Liouville Integrable Systems; Lie Algebras; Poisson Manifolds; Integrable Systems on Poisson Manifolds --
Part II: Algebraic Completely Integrable Systems; The Geometry of Abelian Varieties; A.c.i. Systems; Weight Homogeneous A.c.i. Systems --
Part III: Examples; Integrable Geodesic Flow on SO(4); Periodic Toda Lattices Associated to Cartan Matrices; Integrable Spinning Tops --
References --
Index.
Series Title: Ergebnisse der Mathematik und ihrer Grenzgebiete, 3. Folge. A Series of Modern Surveys in Mathematics, 47.
Responsibility: by Mark Adler, Pierre Moerbeke, Pol Vanhaecke.

Abstract:

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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From the reviews of the first edition:"The aim of this book is to explain `how algebraic geometry, Lie theory and Painleve analysis can be used to explicitly solve integrable differential equations'. Read more...

 
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