The proof of the stability theorem
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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.
KeywordsStability Theorem Small Orbit Homotopy Method Homological Equation Large Orbit
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