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Overview"In the first volume of this survey (Arnol'd et al. (1988), hereafter cited as ""EMS 6"") we acquainted the reader with the basic concepts and methods of the theory of singularities of smooth mappings and functions. This theory has numerous applications in mathematics and physics; here we begin describing these applica tions. Nevertheless the present volume is essentially independent of the first one: all of the concepts of singularity theory that we use are introduced in the course of the presentation, and references to EMS 6 are confined to the citation of technical results. Although our main goal is the presentation of analready formulated theory, the readerwill also come upon some comparatively recent results, apparently unknown even to specialists. We pointout some of these results. 2 3 In the consideration of mappings from C into C in§ 3. 6 of Chapter 1, we define the bifurcation diagram of such a mapping, formulate a K(n, 1)-theorem for the complements to the bifurcation diagrams of simple singularities, give the definition of the Mond invariant N in the spirit of ""hunting for invariants"", and we draw the reader's attention to a method of constructing the image of a mapping from the corresponding function on a manifold with boundary. In§ 4. 6 of the same chapter we introduce the concept of a versal deformation of a function with a nonisolated singularity in the dass of functions whose critical sets are arbitrary complete intersections of fixed dimension." Full Product DetailsAuthor: V.I. Arnol'd , J.S. Joel , V.I. Arnol'd , V.V. GoryunovPublisher: Springer-Verlag Berlin and Heidelberg GmbH & Co. KG Imprint: Springer-Verlag Berlin and Heidelberg GmbH & Co. K Edition: Softcover reprint of hardcover 1st ed. 1993 Volume: 39 Dimensions: Width: 15.50cm , Height: 1.30cm , Length: 23.50cm Weight: 0.454kg ISBN: 9783642081019ISBN 10: 3642081010 Pages: 238 Publication Date: 19 October 2010 Audience: Professional and scholarly , Professional and scholarly , Professional & Vocational , Professional & Vocational Format: Paperback Publisher's Status: Active Availability: In Print  This item will be ordered in for you from one of our suppliers. Upon receipt, we will promptly dispatch it out to you. For in store availability, please contact us. Table of ContentsReviewsV.I. Arnol'd, V.V. Goryunov, O.V. Lyashko, V.A. Vasil'ev, and V.I. Arnol'd (eds.) Dynamical Systems VIII The book contains a huge amount of information from all the branches of Singularity Theory, presented in a very attractive way, with lots of inspiring pictures. -ZENTRALBLATT MATH V.I. Arnol'd, V.V. Goryunov, O.V. Lyashko, V.A. Vasil'ev, and V.I. Arnol'd (eds.) Dynamical Systems VIII The book contains a huge amount of information from all the branches of Singularity Theory, presented in a very attractive way, with lots of inspiring pictures. --ZENTRALBLATT MATH Author InformationTab Content 6Author Website:Countries AvailableAll regions |
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