This paper concerns the description of some properties of p-dimensional invertible real maps
Tb, turning into a (p - 1)-dimensional non invertible ones T0, p = 2, 3, when a parameter b of
the first map is equal to a critical value, say b=0. Then it is said that the noninvertible map is
embedded into the invertible one. More particularly properties of the stable, and the unstable
manifolds of a saddle fixed point are considered in relation with this embedding. This is made
by introducing the notion of folding as resulting from the crossing through a commutation curve
when p = 2, or a commutation surface when p = 3
