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

Manifold 

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Copyright information

© Birkhäuser Boston, Inc. 1985

Authors and Affiliations

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

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