Abstract:

The structural stability of vector fields with impasse regular curves on $mathbb{S}^2$ is studied and a version of the Peixoto's Theorem is established.

Moreover a global analysis of normal forms of the constrained systems $Ax.x' = F(x)$, $x in mathbb{R}^3$, $Ain M(3)$ and $F : mathbb {R}^3 ightarrow mathbb{R}^3$ in the Poicaré ball (i.e. in the compactification of $mathbb {R}^3$ with the sphere $mathbb {S}^2$ of the infinity) is made.

The talk is based on a joint work with Claudio Buzzi and Paulo Ricardo da Silva.