Twist Mappings and Their Applications

In his 1890 analysis of the stability of orbits in the classical three body problem, Poincaré introduced basic ideas about twist maps of the annulus. One hundred years later, the study of twist maps is an important area of dynamical systems theory. Based on a recent IMA workshop, Twist Mappings and Their Applications presents some of the most up-to-date developments in this area by leading figures in the field. The topics in this volume range from the exposition of new tools used to study the area-preserving map of the two-dimensional annulus to analogues of twist maps for higher dimensional annuli and their applications to dynamical systems. In addition, the text incorporates articles which use such innovations to shed light on the original questions of stability in mechanical systems. This book will be of interest to mathematicians, physicists and engineers wishing to keep abreast of this fundamental and evolving area of classical mechanics. It could also be useful to students, scientists and scholars interested in studying the practice of manifold analysis.