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One service mathematics has rendered the 'Ht moi, ... Ii j'avait so comment en revenir, je ny _ais point aile':' human race. It has put common sense back Jules Verne where it belongs, on the topmost shelf neJll to the dusty canister labelled 'discarded non The series is diwrgent; therefore we may be sense' . ble to do something with it. Eric T. Bell O. H eniside Mathematics is a tool for thought. A highly necessary tool in a world where both feedback and non linearities abound. Similarly, alI kinds of parts of mathematics serve as tools for other parts and for other sciences. Applying a simple rewriting rule to the quote on the right above one finds such statements as: 'One service topology has rendered mathematical physics .. .'; 'One service logic has rendered com puter science .. .'; 'One service category theory has rendered mathematics .. .'. All arguably true. And all statements obtainable this way form part of the raison d't!tre of this series.
Table des matières
Table of Content.- I. Dynamical Systems and Statistical Mechanics.- Fast Dynamo for Some Anosov Flows.- How Horseshoes Are Created.- Fine Structure of Universal Cantor Sets.- Hamiltonian Chaos in a Laser Damage Model.- Periodic Modulation of a Logistic Oscillator.- Quantum Spin Chains with Residual Entropy.- Quantum Fluctuations and Linear Response Theory.- Non-Commutative Large Deviations and Applications.- Squeezing in the Su(1,1) Group.- Full Scaling and Real-Space Renormalization.- Sand Piles, Combinatorial Games and Cellular Automata.- II. Stochastic Effects on Dynamical Systems.- Nonequilibrium Potentials in Spatially Extended Pattern Forming Systems.- Passage Time Description of Dynamical Processes.- Stochastic Processes Driven by Colored Noise: A Path Integral Point of View.- Effect of Noise on a Hopf Bifurcation.- Some Properties of Quasi Stationary Distributions in the Birth and Death Chains: A Dynamical Approach.- Photon Noise Reduction in Light Sources.- III. Instabilities in Nonequilibrium Systems.- Spatio-Temporal Properties of Centrifugal Instabilities.- Shape of Stationary and Travelling Cells in The Printer's Instability.- Secondary Instability of Cellular Structures in Directional Solidification.- Velocity Field Structure and Semiquantitative Analysis Of Tracer Dispersion in a Taylor-Vortex Flow of Wide Gap.- Lasers as a Test Bench for Theories of Non-Equilibrium Structures.- Mean Field Theory of Canonical Spinodal Instabilities.- Periodic (Layered) Structures under Constraint.- Transitions Between Patterns of Different Symmetries.- Direct Simulation of Three-Dimensional Turbulence.- Transition Between Different Symmetries in Convection.- Shallow Surface Waves in a Convecting Fluid.- An Exact Model of Resistive Convection in a Cylindrical Plasma.-Energy Method in the Stability of Viscoelastic Fluid.- Solitary Waves, Topological Defects and Their Interactions in Systems with Translational and Galilean Invariance.- Dynamics of Nonlinear SchrÖDinger Defects in Three Dimensions.- Dynamics of Spiral Defects in Two Dimensional Extendedsystems.- Fragmentation.- Qualitative Theory of Defects in Non-Equilibrium Systems.
