Let $\gamma$ be an integral solution of an analytic real vector field $\xi$ defined in a neighbordhood of $0\in {ℝ}^3$. Suppose that $\gamma$ has a single limit point, $\omega \left(\gamma \right)=\left\{0\right\}$. We say that $\gamma$ is non oscillating if, for any analytic surface $H$, either $\gamma$ is contained in $H$ or $\gamma$ cuts $H$ only finitely many times. In this paper we give a sufficient condition for $\gamma$ to be non oscillating. It is established in terms of the existence of “generalized iterated tangents”, i.e. the existence of a single limit point for any transform property for...

We show that every small resolution of a 3-dimensional terminal hypersurface singularity can occur on a non-embeddable $1$-convex manifold.We give an explicit example of a non-embeddable manifold containing an irreducible exceptional rational curve with normal bundle of type $(1,-3)$. To this end we study small resolutions of $c{D}_4$-singularities.