Titlebook: Catastrophe Theory; Vladimir Igorevich Arnold Book 19862nd edition Springer-Verlag Berlin Heidelberg 1986 Bifurcations.Catastrophe Theory.

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Singularities in Optimization Problems: the Maximum Function,tion, control theory and decision theory. For instance, suppose we have to find . such that the value of a function .(.) is maximal (Fig. 46). Under a smooth change of the function the optimal solution changes with a jump from one of the two competing maxima (.) to the other (.).

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Symplectic and Contact Geometry, the various singularities in optimization and variational calculus problems) become understandable only within the framework of the geometry of symplectic and contact manifolds, which is refreshingly unlike the usual geometries of Euclid, Lobachevskij and Riemann.

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