Algebraic integrability, Painlevé geometry and Lie algebras

Mark Adler, Pierre van Moerbeke, Pol Vanhaecke

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 Painleve 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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  • 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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書名 Algebraic integrability, Painlevé geometry and Lie algebras
著作者等 Adler, Mark
Van Moerbeke, Pierre
Vanhaecke, Pol
Moerbeke Pierre
シリーズ名 Ergebnisse der Mathematik und ihrer Grenzgebiete
出版元 Springer
刊行年月 c2004
ページ数 xii, 483 p.
大きさ 25 cm
ISBN 354022470X
NCID BA68717634
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言語 英語
出版国 ドイツ