Constrained equations with impasse points (Q1378677)

Consider differential systems of the form \((*)\) \(f(z) \dot{z} = h(z)\) where \(f\) is a smooth (in the sense of \(C^\infty\)) real function and \(h\) is a smooth vector field on \(\mathbb{R}^m\). A point \(z_0\) is called an impasse point of \((*)\) if it satisfies \(f (z_0 )=0\), \(f' (z_0) h (z_0 ) \neq 0\). The author gives normal forms for the germs at impasse points for generic pairs \((f,h)\).