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.

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