In this paper we study functions and vector fields with isolated singularities on a C(ℂPn)-singular manifold. In general, a C(ℂPn)-singular manifold is obtained from a smooth (2n + 1)-manifold with boundary which is a ...

We address the following conjecture about the existence of common zeros for commuting vector fields in dimension 3: if are two commuting vector fields on a 3-manifold , and is a relatively compact open such that does not ...

In this paper we study functions and vector fields with isolated singularities on a C(CPn)-singular manifold. In general, a C(CPn)-singular manifold is obtained from a smooth (2n+1) -manifold with boundary which is a ...

For a two-dimensional compact oriented Riemannian manifold (M,g), and a vector field V on M, the Hopf–Poincaré theorem combined with the Gauss–Bonnet theorem gives the Gauss–Bonnet–Hopf–Poincaré (GBHP) formula: ∑z∈Z(V)indz(V)= ...

This paper uses the qualitative theory of differential equations to analyse/design the dynamic behaviour of control systems. In particular, the Poincaré compactification and the Poincaré - Hopf theorem are used for analysing ...