Types of change of stability and corresponding types of bifurcations
The goal of this paper is to show connections between change of stability and different types of bifurcation. In particular the authors adress the case where an invariant set \(M\) is unstable (for instance of saddle-type) for a certain parameter value \(\lambda_0\), and stable for certain nearby values. Two types of bifurcations are considered: ``extracritical'', that is splitting of the set \(M\) as \(\lambda\) passes the value \(\lambda_0\), and ``critical'', a term which refers to the accumulation of closed invariant sets at \(\lambda= \lambda_0\). Moreover, two kinds of change of stability are considered, corresponding to the presence or absence of a certain generalized equistability property for \(\lambda\neq \lambda_0\).
scientific article; zbMATH DE number 1492607