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Our aim is to study germs of singularities of vector fields in ℝ3 whose linear part generates a 1-parameter group of rotations. We describe how under very general conditions the ∞-jet of the vector field can give information as well on the existence of an invariant C℞ line and invariant C℞ cones as on the topology of the singularity. In finite codimension the weak-C°-equivalence class (which...
We give a detailed and simplified proof of a theorem of Yu. S. Il'yashenko which concerns the uniqueness of certain limit cycles. A slightly extended version of this theorem is then applied to a global Hopf bifurcation problem treated by Keener.
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