The Transition to Chaos

Abstract

This book is about dynamics. More specifically, it is about the dynamics of conservative classical and quantum systems and perhaps even about the dynamics of stochastic systems. Even though classical and quantum mechanics are rather old subjects by now (classical mechanics is over 300 years old and quantum mechanics is over 80 years old), the surprising fact is that the mechanisms affecting their dynamical evolution have only recently been understood. With this book we hope to present, in as simple and coherent a manner as possible, the basic mechanisms determining the dynamical evolution of classical and quantum systems. At the end of the book (Chapter 10), we will also make a few comments about stochastic dynamics. The book is divided into three parts; Chapters 2 through 4 deal with the theory of nonlinear classical conservative systems, while Chapters 5 through 9 deal with quantum systems. In Chapter 10, we shall discuss some recent work on stochastic systems. In the present chapter, we give a brief overview of the material contained in the remainder of the book.