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Stability and infinitesimal stability

  • V. I. Arnold
  • S. M. Gusein-Zade
  • A. N. Varchenko
Part of the Monographs in Mathematics book series (MMA, volume 82)

Abstract

In this Chapter a linearisation method is described for determining whether a given differentiable map-germ is stable. The gist of the method consists in reducing the question to the linear problem of infinitesimal stability and to the practically more easily solved problem of infinitesimal V-stability. We develop the technique necessary for the foundation of the method and apply it to the simplest situation, proving a theorem about the equivalence of a function to its Taylor polynomial in a neighbourhood of a critical point of finite multiplicity.

Keywords

Cross Ratio Homotopy Method Taylor Polynomial Homological Equation Local Diffeomorphism 
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

© Birkhäuser Boston, Inc. 1985

Authors and Affiliations

  • V. I. Arnold
  • S. M. Gusein-Zade
  • A. N. Varchenko

There are no affiliations available

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