Abstract
This paper deals with a class of Takens–Bogdanov (TB) points (invariant subspace-breaking TB points) which break the symmetry of an equivariant mapping. A degeneracy of this class is considered; specifically, the transcritical branching is violated due to an additional condition upon the bifurcation equation. It results in a definition of TB points with (bifurcation) codimension $ = 2$. A computer-aided asymptotic analysis of these points under two-dimensional perturbations is proposed and demonstrated in an example. Numerical applications of first-order analytical predictors of “lower” singularities (Hopf points, Takens–Bogdanov points, etc.) which are due to a given perturbation are discussed.
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