On the Embedding of a (p-1)-Dimensional Noninvertible Map into a p-Dimensional Invertible Map (p=2,3)

Abstract

This paper concerns the description of some properties of p-dimensional invertible real maps Tb, turning into a (p-1)-dimensional noninvertible 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.