The Kowalevski Property

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.