Algebraic integrability, Painlevé geometry and Lie algebras
By: Mark Adler, Pierre van Moerbeke, Pol Vanhaecke.
Contributors: Moerbeke, Pierre van.; Vanhaecke, Pol, 1963-
Series: Ergebnisse der Mathematik und ihrer Grenzgebiete,; 3. Folge, v. 47 =; A series of modern surveys in mathematics; Ergebnisse der Mathematik und ihrer Grenzgebiete ;; 3. Folge, Bd. 47.
Publisher: Springer
Published: 2004
Place of publication: Berlin; New York
Language: eng
Number of pages: 483
Subjects: Lie algebras; Differential equations; Geometry, Algebraic; Painlevé equations
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 PainlevÃ© 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.
Notes: Includes bibliographical references (p. [469]-478) and index.