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

• Κύριοι συγγραφείς: Arnold, V.I (Συγγραφέας), Gusein-Zade, S.M (Συγγραφέας), Varchenko, A.N (Συγγραφέας)
• Συγγραφή απο Οργανισμό/Αρχή: SpringerLink (Online service)
• Μορφή: Ηλεκτρονική πηγή Ηλ. βιβλίο
• Γλώσσα: English
• Έκδοση: Boston : Birkhäuser Boston : Imprint: Birkhäuser, 2012.
• Σειρά: Modern Birkhäuser Classics
• Θέματα: Mathematics.; Algebraic geometry.; Topological groups.; Lie groups.; Mathematical analysis.; Analysis (Mathematics).; Applied mathematics.; Engineering mathematics.; Differential geometry.; Manifolds (Mathematics).; Complex manifolds.; Analysis.; Algebraic Geometry.; Differential Geometry.; Topological Groups, Lie Groups.; Manifolds and Cell Complexes (incl. Diff.Topology).; Applications of Mathematics.

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 softcov...

Πίνακας περιεχομένων:

• 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.