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AuthorArnold, V. I. author
TitleSingularity Theory I [electronic resource] / by V. I. Arnold, V. V. Goryunov, O. V. Lyashko, V. A. Vasil'ev
ImprintBerlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 1998
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Descript V, 245 p. 1 illus. online resource


From the reviews of the first printing of this book, published as volume 6 of the Encyclopaedia of Mathematical Sciences: "... My general impression is of a particularly nice book, with a well-balanced bibliography, recommended!" Medelingen van Het Wiskundig Genootschap, 1995 "... The authors offer here an up to date guide to the topic and its main applications, including a number of new results. It is very convenient for the reader, a carefully prepared and extensive bibliography ... makes it easy to find the necessary details when needed. The books (EMS 6 and EMS 39) describe a lot of interesting topics. ... Both volumes are a very valuable addition to the library of any mathematician or physicist interested in modern mathematical analysis." European Mathematical Society Newsletter, 1994 "...The authors are recognized experts in their fields and so are ideal choices to write such a survey. ...The text of the book is liberally sprinkled with illustrative examples and so the style is not heavy going or turgid... The bibliography is very good and extremely large ..." IMS Bulletin, 1995


1. Critical Points of Functions -- 1. Invariants of Critical Points -- 2. The Classification of Critical Points -- 3. Reduction to Normal Forms -- 2. Monodromy Groups of Critical Points -- 1. The Picard-Lefschetz Theory -- 2. Dynkin Diagrams and Monodromy Groups -- 3. Complex Monodromy and Period Maps -- 4. The Mixed Hodge Structure in the Vanishing Cohomology -- 5. Simple Singularities -- 6. Topology of Complements of Discriminants of Singularities -- 3. Basic Properties of Maps -- 1. Stable Maps and Maps of Finite Multiplicity -- 2. Finite Determinacy of Map-Germs, and Their Versal Deformations -- 3. The Topological Equivalence -- 4. The Global Theory of Singularities -- 1. Thom Polynomials for Maps of Smooth Manifolds -- 2. Integer Characteristic Classes and Universal Complexes of Singularities -- 3. Multiple Points and Multisingularities -- 4. Spaces of Functions with Critical Points of Mild Complexity -- 5. Elimination of Singularities and Solution of Differential Conditions -- 6. Tangential Singularities and Vanishing Inflexions -- References -- Author Index

Mathematics Algebraic geometry Mathematical analysis Analysis (Mathematics) Mathematics Algebraic Geometry Analysis


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