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

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...

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Detalles Bibliográficos
Clasificación:Libro Electrónico
Autores principales: Arnold, V.I (Autor), Gusein-Zade, S.M (Autor), Varchenko, Alexander N. (Autor)
Autor Corporativo: SpringerLink (Online service)
Formato: Electrónico eBook
Idioma:Inglés
Publicado: Boston, MA : Birkhäuser Boston : Imprint: Birkhäuser, 2012.
Edición:1st ed. 2012.
Colección:Modern Birkhäuser Classics,
Temas:
Mathematical analysis.
Algebraic geometry.
Geometry, Differential.
Topological groups.
Lie groups.
Manifolds (Mathematics).
Mathematics.
Analysis.
Algebraic Geometry.
Differential Geometry.
Topological Groups and Lie Groups.
Manifolds and Cell Complexes.
Applications of Mathematics.
Acceso en línea:Texto Completo
Tabla de Contenidos:
  • 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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