The Kowalevski Property

The Kowalevski Property

by Vadim B. Kuznetsov
     
 

ISBN-10: 0821828851

ISBN-13: 9780821828854

Pub. Date: 07/16/2002

Publisher: American Mathematical Society

This book is a collection of survey articles on 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 subject areas in depth. It provides a broad overview of research from the nineteenth century to the present. The book

Overview

This book is a collection of survey articles on 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 subject areas in depth. It provides a broad overview of research from the nineteenth century to the present. The book begins with two historical papers by R. L. Cooke on Kowalevski's life and work. Following are research surveys on integrability issues in differential and algebraic geometry, classical complex analysis, discrete mathematics, spinning tops, Painleve equations, global analysis on manifolds, special functions, etc. It concludes with Kowalevski's famous paper published in Acta Mathematica in 1889. 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.

Product Details

ISBN-13:
9780821828854
Publisher:
American Mathematical Society
Publication date:
07/16/2002
Series:
CRM Proceedings and Lecture Notes Series , #32
Pages:
372

Table of Contents

Prefacevii
List of Participantsxi
The Life of S. V. Kovalevskaya1
Kovalevskaya's Mathematical Work21
The KZB Connection: Parametrizations, Flat Sections and q-Deformation41
Jacobians of Singularized Spectral Curves and Completely Integrable Systems59
The q-Hypergeometric Equation, Askey-Wilson Type Solitons and Rational Curves With Singularities69
Quantum Discrete Soliton Equations93
Dual Algebras of Differential Operators121
A Link Between Two Fundamental Contributions of Kowalevski149
Monodromy Deformation Approach to the Scaling Limit of the Painleve First Equation157
Kowalevski top revisited181
Some Algebro-Geometric Integrable Systems Versus Classical Ones197
Painleve Sixth Equation as Isomonodromic Deformations Equation of an Irregular System219
Euler Characteristics of Theta Divisors of Jacobians for Spectral Curves239
Reduction Theory, Elliptic Solitons and Integrable Systems247
Schwarzian Derivatives and Uniformization271
Elliptic Solitons and Heun's Equation287
Generalized Kowalevski Top: New Integrable Cases on e(3) and so(4)307
Sur le probleme de la rotation d'un corps solide autour d'un point fixe315

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