We present here a selection of the seminars given at the Second International Workshop on Instabilities and Nonequilibrium Structures in Valparaiso, Chile, in December 1987. The Workshop was organized by Facultad de Ciencias Fisicas y Matematicas of Universidad de Chile and by Universidad Tecnica Federico Santa Maria where it took place. This periodic meeting takes place every two years in Chile and aims to contribute to the efforts of Latin America towards the development of scientific research. This development is certainly a necessary condition for progress in our countries and we thank our lecturers for their warm collaboration to fulfill this need. We are also very much indebted to the Chilean Academy of Sciences for sponsoring officially this Workshop. We thank also our sponsors and supporters for their valuable help, and most especially the Scientific Cooperation Program of France, UNESCO, Ministerio de Educaci6n of Chile and Fundaci6n Andes. We are grateful to Professor Michiel Hazewinkel for including this book in his series and to Dr. David Larner of Kluwer for his continuous interest and support to this project.

I. Dynamical Systems and Statistical Mechanics.- Ergodic Theory and Sobolev Spaces.- Absolutely Continuous Invariant Measure for Expanding Pick Maps of the Interval Except at a Marginal Fixed Point.- Transport of Passive Scalars: Kam Surfaces and Diffusion in three-Dimensional Liouvillian Maps.- Periodic Orbits of Maps on the Disk With Zero Entropy.- Periodically and Randomly Modulated Non Linear Processes.- The Gap Road to Chaos and its Main Characteristics.- Potts Model and Automata Networks.- Cellular-Automata Fluids.- Cylinder Distribution of Thermodynamic Limit on Bethe Lattices.- Rigorous Results About Detailed Balance and Critical Slowing Down.- Quantum Chaos.- Reduction of Quantum Noise n Atomic Systems.- II. Instabilities in Nonequilibrium Systems.- Direct Simulation of Two-Dimensional Turbulence.- Transition to Turbulence in Open Flows. A "metaphoric" approach.- The Role of Topological Defects in Subcritical Bifurcations 189 P. Coullet.- Vortex Variations.- Oscillatory Instabilities in Benard-Marangoni Convection in a Fluid Bounded Above by A Free Surface.- Parametric Instabilities.- Spatio-Temporal Radiation Pattern of A High Energy Electron.- Stability of Taylor-Couette Flow with Radial Heating.- Flow Field Effects on Dynamical Instabilities.- Instabilities in Non-Autonomous Systems.- Polynomial Approximations for Nonequilibrium Potentials Near Instabilities.