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  • 1
    Berlin ; Heidelberg : Springer
    Description / Table of Contents: INTRODUCTION Theoretical modelling and the use of mathematical methods are presently gaining in importance since progress in both geology and mathematics offers new possibilities to combine both fields. Most geological problems are inherently geometrical and morphological, and, therefore, amenable to a classification of forms from a "Gestalt point of view". Geometrical objects have to possess an inherent stability in order to preserve their essential quality under slight deformations. Otherwise, we could hardly conceive of them or describe them, and today's observation would not reproduce yesterday's result (DANGELMAYR & GÜTTINGER, 1982). This principle has become known as "structural stability" (THOM, 1975), i.e. the persistence of a phenomenon under all allowed perturbations. Stability is also, of course, an assumption of classical Newtonian physics, which is essentially the theory of various kinds of smooth behavior (POSTON &STEWART, 1978). However, things sometimes "jump". A new species with a different morphology appears suddenly in the paleontological record (EI.DREDGE & GOULD, 1972), a fault develops, a landslide moves, a computer program becomes unstable with a certain data configuration, etc. It is, surprisingly, the topological approach which permits the study of a broad range of such phenomena in a coherent manner (POSTON & STEWART, 1978; LU, 1976; STEWART, 1982). The universal singularities and bifurcation processes derived from the concept of structural stabiIity determine the spontaneous formation of qualitatively similar spatio-temporal structures in systems of various geneses exhibiting critical behavior (DANGELMAYR & GÜTTINGER, 1982; THOM, 1975; POSTON & STEWART, 1978; GÜTTINGER & EIKEMEIER, t979; STEWART, 1981). In addition, this return to a "geometrization of phenomena"-- after decades of algorithmization-- comes much closer to the geologist's intuitive geometric reasoning. It is the aim of this study to elucidate, by examples, how the qualitative geometrical approach allows one to classify forms and to control the behavior of complex computer algorithms...
    Pages: Online-Ressource (229 Seiten)
    ISBN: 9783540139836
    Language: English
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