Abstract
Presents a broadly based discussion of 'catastrophe theory,' a mathematical discipline commonly associated with the names of Thom and Zeeman, placing emphasis on the development feedback between the mathematics and its applications, especially to the physical sciences. The author aims to present a typical selection of current work. Among the more prominent of the concepts that have emerged from this work are co-dimension, determinacy, unfoldings and organising centres. He shows, using specific applications as motivation, how these concepts may be used, and generalised to areas not obviously within the formal purview of 'catastrophe theory' as it is often presented. Structural stability, a concept from topological dynamics that provides a philosophical background for catastrophe theory, is also discussed. The mathematics of the subject has advanced considerably over the past decade, and in doing so has lost many of its original limitations. Some of these new directions are exhibited. On occasion, the catastrophe-theoretic methods are compared to more traditional ones.
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