Introduction to Symplectic Topology

Abstract Symplectic structures underlie the equations of classical mechanics and their properties are reflected in the behaviour of a wide rane of physical systems. Over the years much detailed knowledge has accumulated about the behaviour of particular systems, but the modern global theory of sympletic topology has just emerged. Powerful new methods in analysis and topology have led to a series of striking results, such as Gromov's flexiblity theorem on the existance of symplectic structures, and the various proofs of the Arnold conjectures on the number of fixed points of a symplectic map. This book contains an introduction to the subject, which will acquaint the reader with almost all the new methods in the field, providing proofs of the simplier versions of the most important new theorems. The deepest theorems in the book are proved by a new finite dimensional variational analysis of Hofer-Zehnder.