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Versal deformations

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

Abstract

Ordinarily in the consideration of all possible singularities the principal interest focusses on the generic case, since all the more complicated singularities may be got rid of by a small perturbation. For example, a generic function has only nondegenerate critical points; degenerate critical points, like the critical point of the function x3, decompose into nondegenerate ones under a suitable small deformation, for example x3 - εX.

Keywords

Normal Form Tangent Space Phase Curve Versal Deformation Jordan Normal Form 
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.

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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

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