Subordinate Šil'nikov bifurcations near some singularities of vector fields having low codimension

Abstract

A specific singularity of a vector field on [formula-omitted] is considered, of codimension 2 in the dissipative case and of codimension 1 in the conservative case. In both contexts in generic unfoldings the existence is proved of subordinate Šil'nikov bifurcations, which have codimension 1. Special attention is paid to the C∞-flatness of this subordinate phenomenon. © 1984, Cambridge University Press. All rights reserved.