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

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Abstract
A specific singularity of a vector field on 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.
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