Algebraic Integrability, Painlevé Geometry...

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Sprache: Englisch

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Beschreibung

In the early 70's and 80's the field of integrable systems was in its prime youth: results and ideas were mushrooming all over the world. It was during the roaring 70's and 80's that a first version of the book was born, based on our research and on lectures which each of us had given. We owe many ideas to our colleagues Teruhisa Matsusaka and David Mumford, and to our inspiring graduate students (Constantin Bechlivanidis, Luc Haine, Ahmed Lesfari, Andrew McDaniel, Luis Piovan and Pol Vanhaecke). As it stood, our first version lacked rigor and precision, was rough, dis connected and incomplete. . . In the early 90's new problems appeared on the horizon and the project came to a complete standstill, ultimately con fined to a floppy. A few years ago, under the impulse of Pol Vanhaecke, the project was revived and gained real momentum due to his insight, vision and determination. The leap from the old to the new version is gigantic. The book is designed as a teaching textbook and is aimed at a wide read ership of mathematicians and physicists, graduate students and professionals.

Zusammenfassung

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 to construct the algebraic tori on which they linearize

The book is reasonably self-contained and presents numerous examples

Includes supplementary material: [...]

Inhaltsverzeichnis

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.

Details

Erscheinungsjahr:	2004
Fachbereich:	Arithmetik & Algebra
Genre:	Mathematik
Rubrik:	Naturwissenschaften & Technik
Medium:	Buch
Reihe:	Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics
Inhalt:	xii 484 S.
ISBN-13:	9783540224709
ISBN-10:	354022470X
Sprache:	Englisch
Herstellernummer:	10969434
Ausstattung / Beilage:	HC runder Rücken kaschiert
Einband:	Gebunden
Autor:	Adler, Mark Vanhaecke, Pol Moerbeke, Pierre van
Hersteller:	Springer-Verlag GmbH Springer Berlin Heidelberg Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics
Maße:	241 x 160 x 32 mm
Von/Mit:	Mark Adler (u. a.)
Erscheinungsdatum:	01.09.2004
Gewicht:	0,91 kg