CRM Proceedings & Lecture Notes 2002; 372 pp; softcover Volume: 32 ISBN10: 0821828851 ISBN13: 9780821828854 List Price: US$138 Member Price: US$110.40 Order Code: CRMP/32
 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 copublished 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  R. L. Cooke  The life of S. V. Kovalevskaya
 R. L. Cooke  Kovalevskaya's mathematical work
 B. Enriquez  The KZB connection: Parametrizations, flat sections and \(q\)deformation
 L. Gavrilov  Jacobians of singularized spectral curves and completely integrable systems
 L. Haine  The \(q\)hypergeometric equation, AskeyWilson type solitons and rational curves with singularities
 K. Hikami  Quantum discrete soliton equations
 E. I. Horozov  Dual algebras of differential operators
 J.S. Hu and M. Yan  A link between two fundamental contributions of Kowalevski
 A. A. Kapaev  Monodromy deformation approach to the scaling limit of the Painlevé first equation
 V. B. Kuznetsov  Kowalevski top revisited
 D. Markushevich  Some algebrogeometric integrable systems versus classical ones
 M. Mazzocco  Painlevé sixth equation as isomonodromic deformations equation of an irregular system
 A. Nakayashiki and F. A. Smirnov  Euler characteristics of theta divisors of Jacobians for spectral curves
 E. Previato  Reduction theory, elliptic solitons and integrable systems
 T. Sasaki and M. Yoshida  Schwarzian derivatives and uniformization
 A. O. Smirnov  Elliptic solitons and Heun's equation
 V. V. Sokolov  Generalized Kowalevski top: New integrable cases on \(e\)(3) and so(4)
Reprint of the Original Paper  S. Kowalevski  Sur le problème de la rotation d'un corps solide autour d'un point fixe
