The Kowalevski Property
About this Title
Vadim B. Kuznetsov, University of Leeds, Leeds, UK, Editor
Publication: CRM Proceedings and Lecture Notes
Publication Year: 2002; Volume 32
ISBNs: 978-0-8218-2885-4 (print); 978-1-4704-3946-0 (online)
MathSciNet review: MR1916772
MSC: Primary 37-06; Secondary 00B25, 14-06, 34M35, 34M55, 37J35, 37K20, 70H06
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, Painlevé 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.
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 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, Askey-Wilson 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 algebro-geometric 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