Softcover ISBN:  9780821828854 
Product Code:  CRMP/32 
List Price:  $138.00 
MAA Member Price:  $124.20 
AMS Member Price:  $110.40 
Electronic ISBN:  9781470439460 
Product Code:  CRMP/32.E 
List Price:  $138.00 
MAA Member Price:  $124.20 
AMS Member Price:  $110.40 

Book DetailsCRM Proceedings & Lecture NotesVolume: 32; 2002; 372 ppMSC: Primary 14; 17; 37; 35; 70; 81;
This book is a collection of survey articles on several topics related to the general notion of integrability. It stems from a workshop on “Mathematical Methods of Regular Dynamics” dedicated to Sophie Kowalevski. Leading experts introduce corresponding areas in depth. The book provides a broad overview of research, from the pioneering work of the nineteenth century to the developments of the 1970s through the present.
The book begins with two historical papers by R. L. Cooke on Kowalevski's life and work. Following are 15 research surveys on integrability issues in differential and algebraic geometry, classical complex analysis, discrete mathematics, spinning tops, Painlevé equations, global analysis on manifolds, special functions, etc. It concludes with Kowalevski's famous paper published in Acta Mathematica in 1889, “Sur le problème de la rotation d'un corps solide autour d'un point fixe”.
The book is suitable for graduate students in pure and applied mathematics, the general mathematical audience studying integrability, and research mathematicians interested in differential and algebraic geometry, analysis, and special functions.ReadershipGraduate students in pure and applied mathematics, the general mathematical audience studying integrability, and research mathematicians interested in differential and algebraic geometry, analysis, and special functions.

Table of Contents

Chapters

The life of S. V. Kovalevskaya

Kovalevskaya’s mathematical work

The KZB connection: Parametrizations, flat sections and $q$deformation

Jacobians of singularized spectral curves and completely integrable systems

The $q$hypergeometric equation, AskeyWilson type solitons and rational curves with singularities

Quantum discrete soliton equations

Dual algebras of differential operators

A link between two fundamental contributions of Kowalevski

Monodromy deformation approach to the scaling limit of the Painlevé first equation

Kowalevski top revisited

Some algebrogeometric integrable systems versus classical ones

Painlevé sixth equation as isomonodromic deformations equation of an irregular system

Euler characteristics of theta divisors of Jacobians for spectral curves

Reduction theory, elliptic solitons and integrable systems

Schwarzian derivatives and uniformization

Elliptic solitons and Heun’s equation

Generalized Kowalevski top: New integrable cases on $e$(3) and so(4)

Reprint of the Original Paper

Sur le problème de la rotation d’un corps solide autour d’un point fixe


RequestsReview Copy – for reviewers who would like to review an AMS bookAccessibility – to request an alternate format of an AMS title
 Book Details
 Table of Contents
 Requests
This book is a collection of survey articles on several topics related to the general notion of integrability. It stems from a workshop on “Mathematical Methods of Regular Dynamics” dedicated to Sophie Kowalevski. Leading experts introduce corresponding areas in depth. The book provides a broad overview of research, from the pioneering work of the nineteenth century to the developments of the 1970s through the present.
The book begins with two historical papers by R. L. Cooke on Kowalevski's life and work. Following are 15 research surveys on integrability issues in differential and algebraic geometry, classical complex analysis, discrete mathematics, spinning tops, Painlevé equations, global analysis on manifolds, special functions, etc. It concludes with Kowalevski's famous paper published in Acta Mathematica in 1889, “Sur le problème de la rotation d'un corps solide autour d'un point fixe”.
The book is suitable for graduate students in pure and applied mathematics, the general mathematical audience studying integrability, and research mathematicians interested in differential and algebraic geometry, analysis, and special functions.
Graduate students in pure and applied mathematics, the general mathematical audience studying integrability, and research mathematicians interested in differential and algebraic geometry, analysis, and special functions.

Chapters

The life of S. V. Kovalevskaya

Kovalevskaya’s mathematical work

The KZB connection: Parametrizations, flat sections and $q$deformation

Jacobians of singularized spectral curves and completely integrable systems

The $q$hypergeometric equation, AskeyWilson type solitons and rational curves with singularities

Quantum discrete soliton equations

Dual algebras of differential operators

A link between two fundamental contributions of Kowalevski

Monodromy deformation approach to the scaling limit of the Painlevé first equation

Kowalevski top revisited

Some algebrogeometric integrable systems versus classical ones

Painlevé sixth equation as isomonodromic deformations equation of an irregular system

Euler characteristics of theta divisors of Jacobians for spectral curves

Reduction theory, elliptic solitons and integrable systems

Schwarzian derivatives and uniformization

Elliptic solitons and Heun’s equation

Generalized Kowalevski top: New integrable cases on $e$(3) and so(4)

Reprint of the Original Paper

Sur le problème de la rotation d’un corps solide autour d’un point fixe