In this article we give a geometric classification of the set of quadratic
maps of the plane. The fundamental step is the proof that the restriction of the map to the critica! set is injective, from which it follows that there are finitely many classes of geometrically equivalent maps. In the last sections we apply this geometric knowledge to obtain some simple dynamical properties of a particular family of quadratic maps.
Delgado, J. [et al.]. On the geometry of quadratic maps of the plane. "Publicaciones matemáticas del Uruguay", 2013, vol. 14, p. 120-135.