Abstract:

In this talk we describe the global dynamics of the Benoît system. This system is a polynomial system of degree 2 in $mathbb{R}^3.$ For doing this, we will use the Poincaré compactification of $mathbb{R}^3$ and some first integral that this system has. We shall describe all possible phase portraits of the Benoît system inside each level of first integrals in the Poincaré sphere.