Stability and infinitesimal stability
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.
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