From a differentiable to a real analytic perturbation theory, applications to the Kupka Smale theorems

Abstract

Kupka-Smale like theorems are proven in the real analytic case, using existing perturbation schemes for the smooth case and the heat operator. As a consequence, a topological proof is obtained of Siegel’s theorem on the generic divergence of normal form transformations. © 1986, Cambridge University Press. All rights reserved.