**CRM Proceedings & Lecture Notes**

Volume: 32;
2002;
372 pp;
Softcover

MSC: Primary 14; 17; 37; 35; 70; 81;

Print ISBN: 978-0-8218-2885-4

Product Code: CRMP/32

List Price: $138.00

Individual Member Price: $110.40

**Electronic ISBN: 978-1-4704-3946-0
Product Code: CRMP/32.E**

List Price: $138.00

Individual Member Price: $110.40

# The Kowalevski Property

Share this page *Edited by *
*Vadim B. Kuznetsov*

A co-publication of the AMS and Centre de Recherches Mathématiques

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.

Titles in this series are co-published with the Centre de Recherches Mathématiques.

#### Readership

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.

# Table of Contents

## The Kowalevski Property

- Cover Cover11
- Frontispiece ii3
- Title page iii4
- Contents v6
- Preface vii8
- List of participants, Kowalevski workshop (MMRD), University of Leeds, April 12–15, 2000 xi12
- The life of S. V. Kovalevskaya 114
- Kovalevskaya’s mathematical work 2134
- The KZB connection: Parametrizations, flat sections and 𝑞-deformation 4154
- Jacobians of singularized spectral curves and completely integrable systems 5972
- The 𝑞-hypergeometric equation, Askey-Wilson type solitons and rational curves with singularities 6982
- Quantum discrete soliton equations 93106
- Dual algebras of differential operators 121134
- A link between two fundamental contributions of Kowalevski 149162
- Monodromy deformation approach to the scaling limit of the Painlevé first equation 157170
- Kowalevski top revisited 181194
- Some algebro-geometric integrable systems versus classical ones 197210
- Painlevé sixth equation as isomonodromic deformations equation of an irregular system 219232
- Euler characteristics of theta divisors of Jacobians for spectral curves 239252
- Reduction theory, elliptic solitons and integrable systems 247260
- Schwarzian derivatives and uniformization 271284
- Elliptic solitons and Heun’s equation 287300
- Generalized Kowalevski top: New integrable cases on 𝑒(3) and so(4) 307320
- Reprint of the Original Paper 315328
- Sur le problème de la rotation d’un corps solide autour d’un point fixe 317330
- Back Cover Back Cover1386