TY  - BOOK
AU  - 
AU  - 
AU  - 
ED  - SpringerLink (Online service)
TI  - Singularities of Differentiable Maps, Volume 1: Classification of Critical Points, Caustics and Wave Fronts 
T2  - Modern Birkhuser Classics
SN  - 9780817683405
AV  - QA299.6-433 
U1  - 515 23
PY  - 2012///
CY  - Boston
PB  - Birkhuser Boston, Imprint: Birkhuser
KW  - Mathematics
KW  - Geometry, algebraic
KW  - Topological Groups
KW  - Global analysis (Mathematics)
KW  - Global differential geometry
KW  - Cell aggregation
KW  - Analysis
KW  - Algebraic Geometry
KW  - Differential Geometry
KW  - Topological Groups, Lie Groups
KW  - Manifolds and Cell Complexes (incl. Diff.Topology)
KW  - Applications of Mathematics
N1  - 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; ZDB-2-SMA
N2  - Originally published inthe 1980s, Singularities of DifferentiableMaps: The Classificationof Critical Points, Caustics and Wave Fronts was the first oftwovolumes that togetherformed 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 availableand affordableto a global audience of researchers and practitioners. Singularity theory isa far-reaching extension of maxima and minima investigations of differentiable functions, withimplications 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 explorean unparalleled breadth ofapplications
UR  - http://dx.doi.org/10.1007/978-0-8176-8340-5
ER  -