Advertisement

Bifurcations of caustics and wave fronts

  • V. I. Arnold
  • S. M. Gusein-Zade
  • A. N. Varchenko
Chapter
Part of the Modern Birkhäuser Classics book series (MBC)

Abstract

An evolving wave front will not at all moments of time be a generic front: at particular moments it will bifurcate. The study of such bifurcations reduces to a problem on generic singularities in one-parameter families of Legendrian maps. In this Chapter generic one-parameter families of Lagrangian and Legendrian maps are studied. Normal forms are given in those cases where the dimension of the front does not exceed four (or where the dimension of the caustic does not exceed two).

Keywords

Wave Front Maslov Index Lagrangian Manifold Legendrian Curve Legendrian Submanifolds 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Copyright information

© Springer Science+Business Media New York 2012

Authors and Affiliations

  • V. I. Arnold
  • S. M. Gusein-Zade
    • 1
  • A. N. Varchenko
    • 2
  1. 1.Department of Mechanics and MathematicsMoscow State UniversityMoscowRussia
  2. 2.Department of MathematicsThe University of North Carolina at Chapel HillChapel HillUSA

Personalised recommendations