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Singularities of Differentiable Maps, Volume 1: Classification of Critical Points, Caustics and Wave Fronts

Singularities of Differentiable Maps, Volume 1: Classification of Critical Points, Caustics and Wave Fronts
Catalogue Information
Field name Details
Dewey Class 514.72
Title Singularities of Differentiable Maps, Volume 1 ([Ebook]) : Classification of Critical Points, Caustics and Wave Fronts / by V.I. Arnold, S.M. Gusein-Zade, A.N. Varchenko.
Author Arnold, Vladimir Igorevic , 1937-2010
Added Personal Name Gusein-Zade, S.M.
Varchenko, A.N.
Other name(s) SpringerLink (Online service)
Publication Boston : Birkhäuser
, 2012.
Physical Details XII, 282 pages: 67 illus. : online resource.
Series Modern Birkhäuser classics
ISBN 9780817683405
Summary Note Originally published in the 1980s, Singularities of Differentiable Maps: The Classification of Critical Points, Caustics and Wave Fronts was the first of two volumes that together formed a translation of the authors' influential Russian monograph on singularity theory. This uncorrected softcover reprint of the work brings its still-relevant content back into the literature, making it available and affordableâto a global audience of researchers and practitioners. 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 deal with the stability problem for smooth mappings, critical points of smooth functions, and caustics and wave front singularities.  Building on these concepts, the second volume (Monodromy and Asymptotics of Integrals) describes the topological and algebro-geometrical aspects of the theory, including monodromy, intersection forms, oscillatory integrals, asymptotics, and mixed Hodge structures of singularities. Singularities of Differentiable Maps: The Classification of Critical Points, Caustics and Wave Fronts accommodates 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 an unparalleled breadth of applications.:
Contents note Part I. Basic concepts -- The simplest examples -- The classes Sigma I -- The quadratic differential of a map -- The local algebra of a map and the Weierstrass preparation theorem -- The local multiplicity of a holomorphic map -- Stability and infinitesimal stability -- The proof of the stability theorem -- Versal deformations -- The classification of stable germs by genotype -- Review of further results -- Part II. Critical points of smooth functions -- A start to the classification of critical points -- Quasihomogeneous and semiquasihomogeneous singularities -- The classification of quasihomogeneous functions -- Spectral sequences for the reduction to normal forms -- Lists of singularities -- The determinator of singularities -- Real, symmetric and boundary singularities -- Part III. Singularities of caustics and wave fronts -- Lagrangian singularities -- Generating families -- Legendrian singularities -- The classification of Lagrangian and Legendrian singularities -- The bifurcation of caustics and wave fronts -- References -- Further references -- Subject Index.
System details note Online access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users)
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