Catastrophe Theory

§In der dritten Auflage dieses bemerkenswerten Buches hat Arnold den Text gründlich überarbeitet und Aufgaben sowie einen Anhang zur Geschichte der Katastrophentheorie hinzugefügt. Arnold bringt seinen Lesern die Ideen der Katastrophentheorie nahe. Dabei setzt er lediglich voraus, daß der Leser bereit ist, sich auf ein mathematisches Abenteuer einzulassen. This well-known booklet provides an informal survey of applications of singularity theory. Although the first few chapters touch briefly (and critically) on the Thom-Zeeman catastrophe theory, most of the book treats more recent and less controversial aspects, such as bifurcations and stability loss, wavefront propagation, the distribution of matter in the universe, optimization and control problems, visible contours, bypassing an obstacle, symplectic and contact geometry, complex singularities, and the surprising connections between singularities and widely disparate mathematical objects such as regular polyhedra and reflection groups. Readers familiar with the previous editions will find much that is new, e.g. topics like shock waves, implicit differential equations and folded singularities, and interior scattering. §Three new sections give an overview of the history of singularity theory from Leonardo da Vinci to modern times, a discussion of perestroika in terms of the theory of metamorphoses, and a list of 93 problems. Arnold's goal with this edition remains the same: to explain the essence of the results and applications to readers having a minimal mathematical background. All that he asks, is that the reader have an inquiring mind.