Fig. 9

Blow-up of the singular fold. ‘Birds-eye view’ of the upper blown-up sphere \(X^{2}+Y^{2}+E^{2}=1\) in \((X,Y)\)-space. Normal hyperbolicity of the manifolds \(S_{a}\) and \(S_{r}\) is gained at the equator, allowing one to extend them onto the blown-up sphere near singularities \(p_{a}\), respectively, \(p_{r}\). The two additional singularities represent connection to the fast fibre at \(F^{-}\)