Saddle-focus singular cycles and prevalence of hyperbolicity
The main goal of this paper is to show that in the unfolding of a three-dimensional vector field having a saddle-focus singular cycle hyperbolicity is a prevalent phenomenon: that is, the set of parameters corresponding to Axiom A flows has full Lebesgue density at this bifurcation value. Here for the first time nontrivial hyperbolicity is proved for the maximal invariant set for a perturbation of a vector field with a cycle containing a saddle-focus singularity.
scientific article; zbMATH DE number 1199911