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 โ{128}{156}metaphoricโ{128}{157} 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