This volume contains the lecture notes written by the four principal speakers at the C.I.M.E. session on Dynamical Systems held at Montecatini, Italy in June 1994. The goal of the session was to illustrate how methods of dynamical systems can be applied to the study of ordinary and partial differential equations. Topics in random differential equations, singular perturbations, the Conley index theory, and non-linear PDEs were discussed. Readers interested in asymptotic behavior of solutions of ODEs and PDEs and familiar with basic notions of dynamical systems will wish to consult this text.

Since the predecessor to this volume (LNM 1186, Eds. L. Arnold, V. Wihstutz)appeared in 1986, significant progress has been made in the theory and applications of Lyapunov exponents - one of the key concepts of dynamical systems - and in particular, pronounced shifts towards nonlinear and infinite-dimensional systems and engineering applications are observable. This volume opens with an introductory survey article (Arnold/Crauel) followed by 26 original (fully refereed) research papers, some of which have in part survey character. From the Contents: L. Arnold, H. Crauel: Random Dynamical...