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Spectral sequences for the reduction to normal forms

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

Abstract

Here is described a method for the reduction to normal forms, based on a spectral sequence, constructed from the filtration of the Koszul complex determined by the partial derivatives of the function under discussion. We do not use explicitly any properties of spectral sequences or of Koszul complexes, but prove directly everything that is necessary for the practical calculations. The correspondence between our constructions and the ordinary algebraic constructions is described in [18].

Keywords

Normal Form Power Series Spectral Sequence Local Algebra Koszul Complex 
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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