This volume contains some of the lectures presented in June 1994 during the AMS-SIAM Summer Seminar at the Mathematical Sciences Research Institute in Berkeley. The goal of the seminar was to introduce participants to as many interesting and active applications of dynamical systems and probabilistic methods to problems in applied mathematics as possible. As a result, this book covers a great deal of ground. Nevertheless, the pedagogical orientation of the lectures has been retained, and therefore the book will serve as an ideal introduction to these varied and interesting topics.Among the themes explored in this volume are the following: the increasing role of dynamical systems theory in understanding partial differential equations the central importance of certain prototypical equations, such as the complex Ginzburg-Landau, nonlinear Schrodinger, and Korteweg-deVries equations problems in fluid mechanics and the limits of physically motivated heuristic theories of fluids the role of probabilistic methods in studying turbulent phenomena.
