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.
Editorials
Presents 15 surveys of various subjects related to the integrabilty area pioneered by Sophie Kowalevski. Among the topics are Jacobians of singularized spectral curves and completely integrable systems, the monodromy deformation approach to the scaling limit of the Painleve first equation, quantum discrete soliton equations, and generalizations of the Scharzian derivative. Two of the papers sketch Kowalevski's life and contributions to mathematics. A reprint of Kowalevski's 1889 paper in the original French rounds out the book. No index. Annotation c. Book News, Inc., Portland, OR