On the embedding of a (p-1)-dimensional non invertible map into a p-dimensional invertible map

Abstract

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.