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The proof of the stability theorem

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Singularities of Differentiable Maps, Volume 1

Part of the book series: Modern Birkhäuser Classics ((MBC))

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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.

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© 2012 Springer Science+Business Media New York

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Arnold, V.I., Gusein-Zade, S.M., Varchenko, A.N. (2012). The proof of the stability theorem. In: Singularities of Differentiable Maps, Volume 1. Modern Birkhäuser Classics. Birkhäuser, Boston. https://doi.org/10.1007/978-0-8176-8340-5_7

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