Arnold V. Catastrophe Theory 2ed 1986

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Arnold V. Catastrophe Theory 2ed 1986

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Textbook in PDF format The first information on catastrophe theory appeared in the western press about ten years ago. In magazines like "News week" there were reports of a revolution in mathematics, com parable perhaps to Newton's invention of the differential and integral calculus. It was claimed that the new science, catas trophe theory, was much more valuable to mankind than mathematical analysis: while Newtonian theory only consid ers smooth, continuous processes, catastrophe theory provides a universal method for the study of all jump transitions, dis continuities, and sudden qualitative changes. There appeared hundreds of scientific and popular science publications in which catastrophe theory was applied to such diverse targets as, for instance, the study of heart beat, geometrical and phy sical optics, embryology, linguistics, experimental psychology, economics, hydrodynamics, geology, and the theory of ele mentary particles. Among the published works on catastrophe theory are studies of the stability of ships, models for the ac tivity of the brain and mental disorders, for prison uprisings, for the behaviour of investors on the stock exchange, for the influence of alcohol on drivers and for censorship policy with respect to erotic literature. Singularities, Bifurcations, and Catastrophes Whitney's Singularity Theory Applications of Whitney's Theory. A Catastrophe Machine Bifurcations of Equilibrium States Loss of Stability of Equilibrium and of Self-Oscillating Modes of Behaviour Singularities of the Stability Boundary and the Princi ple of the Fragility of Good Things Caustics, Wave Fronts, and Their Metamorphoses The Large-Scale Distribution of Matter in the Universe Singularities in Optimization Problems: the Maximum Function Singularities of the Boundary of Attainability Smooth Surfaces and Their Projections The Problem of Bypassing an Obstacle Symplectic and Contact Geometry Complex Singularities The Mysticism of Catastrophe Theory Bibliographical Comments