The Transition to Chaos

The subjects treated here are part of an active and rapidly growing field of research that touches on the foundations of physics and chemistry. Specifically, the book presents, in as simple and coherent a manner as possible, the basic mechanisms that determine the dynamical evolution of both classical and quantum systems in sufficient generality to include nonlinear phenomena. The book begins with a discussion of Noether's Theorem, integrability, KAM theory, and a definition of chaotic behaviour; it continues with a detailed discussion of area-preserving maps, integrable quantum systems, spectral properties, path integrals, and periodically driven systems; and concludes by showing how to apply the ideas to stochastic systems.