This IMA Volume in Mathematics and its Applications TWIST MAPPINGS AND THEIR APPLICATIONS is based on the proceedings of a workshop which was an integral part of the 1989- 90 IMA program on "Dynamical Systems and their Applications". The workshop brought together many of the leading figures in the modern study of twist maps. We thank Shui-Nee Chow, Martin Golubitsky, Richard McGehee, Ken Meyer, Jiirgen Moser, Clark Robinson, George R. Sell, and Eduard Zehnder for organizing the meeting and, especially, Richard McGehee and Ken Meyer for editing the volume. A vner Friedman Willard Miller, Jr. PREFACE In the 1890 volume of Acta Mathematica, H. Poincare published his prize winning paper on the stability of orbits of the three body problem. In that paper, he introduced some of the basic ideas about twist maps of the annulus. One hun dred years later, the study of twist maps is still an active and important area of dynamical systems theory.

Klappentext

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.

Inhalt

A remark oil the topological entropy and invariant circles of an area preserving twistmap.- The concept of anti-integrability: Definition, theorems and applications to the standard map.- Hypersurfaces without selfintersections in the torus.- The rotation set as a dynamical invariant.- Birkhoff periodic orbits for small perturbations of completely integrable Hamiltonian systems with nondegenerate Hessian.- Physical examples of linked twist maps with chaotic dynamics.- Ghost tori for monotone maps.- Poincaré's proof of Poincaré's last geometric theorem.- Dynamics connected with indefinite normal torsion.- Minimal orbits for small perturbations of completely integrable Hamiltonian systems.