Singularities of Differentiable Maps, Volume 1

Classification of Critical Points, Caustics and Wave Fronts

Häftad, Engelska, 2012

AvV.I. Arnold,S.M. Gusein-Zade,Alexander N. Varchenko,V. I. Arnold,S. M. Gusein-Zade

1 529 kr

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?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.

Produktinformation

Utgivningsdatum2012-05-24
Mått155 x 235 x 22 mm
Vikt600 g
FormatHäftad
SpråkEngelska
SerieModern Birkhäuser Classics
Antal sidor282
Upplaga2012
FörlagBirkhauser Boston Inc
ISBN9780817683399

Tillhör följande kategorier

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.

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