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The proof of the stability theorem

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

Abstract

In this Chapter the stability of an infinitesimally stable map-germ is proved. The proof consists of two parts. Firstly it is proved that the k-jet of an infinitesimally stable germ is stable for sufficiently large k, that is that every sufficiently near map has at a suitably near point a left-right equivalent k-jet. Secondly it is proved that the k-jet of an infinitesimally stable germ is sufficient for sufficiently large k. From these two facts stability clearly follows.

Keywords

Stability Theorem Small Orbit Homotopy Method Homological Equation Large Orbit 
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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