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- Affordable reprint of a classic monograph written by experts in the field
- Provides a uniquely sophisticated investigation of the topics discussed
- Useful for a wide range of applications across disciplines in fields such as differential equations, dynamical systems, optimal control, and optics
- Includes supplementary material: sn.pub/extras
Part of the book series: Modern Birkhäuser Classics (MBC)
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Table of contents (22 chapters)
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The Singularities of Caustics and Wave Fronts
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Front Matter
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Singularities of causties and wave fronts
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Back Matter
About this book
Singularity theory is a far-reaching extension of maxima and minima investigations of differentiable functions, with implications for many different areas of mathematics, engineering (catastrophe theory and the theory of bifurcations), and science. The three parts of this first volume of a two-volume set deal with the stability problem for smooth mappings, critical points of smooth functions, and caustics and wave front singularities. The second volume describes the topological and algebro-geometrical aspects of the theory: monodromy, intersection forms, oscillatory integrals, asymptotics, and mixed Hodge structures of singularities.
The first volume has been adapted for the needs of non-mathematicians, presupposing a limited mathematical background and beginning at an elementary level. With this foundation, the book's sophisticated development permits readers to explore more applications than previous books on singularities.
Authors and Affiliations
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Russian Academy of Sciences, Moscow, Russia
V.I. Arnold
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Moscow State University, Moscow, Russia
S.M. Gusein-Zade
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, Department Mathematics, University of North Carolina, Chapel Hill, USA
A.N. Varchenko
Bibliographic Information
Book Title: Singularities of Differentiable Maps, Volume 1
Book Subtitle: Classification of Critical Points, Caustics and Wave Fronts
Authors: V.I. Arnold, S.M. Gusein-Zade, A.N. Varchenko
Series Title: Modern Birkhäuser Classics
DOI: https://doi.org/10.1007/978-0-8176-8340-5
Publisher: Birkhäuser Boston, MA
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer Science+Business Media New York 2012
Softcover ISBN: 978-0-8176-8339-9Published: 24 May 2012
eBook ISBN: 978-0-8176-8340-5Published: 24 May 2012
Series ISSN: 2197-1803
Series E-ISSN: 2197-1811
Edition Number: 1
Number of Pages: XII, 282
Number of Illustrations: 67 b/w illustrations
Topics: Analysis, Algebraic Geometry, Differential Geometry, Topological Groups, Lie Groups, Manifolds and Cell Complexes (incl. Diff.Topology), Applications of Mathematics
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