Inflated mappings for singularities of codimension \(\leq 2\). (English) Zbl 0633.58013

The organizing centre of an imperfect bifurcation problem \(F(u,\lambda,\alpha)=0\) is linked with a simple root of an auxiliary operator (the inflated mapping of F). Assuming that the particular singularity of the bifurcation equation has codimension \(\leq 2\), the classification of organizing centres is developed in terms of singularities of the germs of smooth mappings \(g: R_ m\times R_ 1\times R_ k\to R_ m\), by defining properly the inflated mapping.
Reviewer: D.Polisevski


58E07 Variational problems in abstract bifurcation theory in infinite-dimensional spaces
58C25 Differentiable maps on manifolds
58K99 Theory of singularities and catastrophe theory
65J15 Numerical solutions to equations with nonlinear operators
14B05 Singularities in algebraic geometry
47J05 Equations involving nonlinear operators (general)
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