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A start to the classification of critical points

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

Abstract

In this Chapter we describe the basic stages in the classification of critical points of holomorphic functions; the results of the classification and the computations necessary for carrying out the various stages are given in the following sections. All the functions under consideration are holomorphic and have a critical point at 0 with critical value 0. By equivalence we mean R-equivalence (two functiongerms are equivalent, if they can be turned into one another under the action of biholomorphic changes of the independent variables).

Keywords

Holomorphic Function Principal Part Basic Stage Marked Index Topological Classification 
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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