Abstract
Assuming a 2-parameter-dependent family of smooth Z 2 -equivariant vector fields, a symmetry-breaking Takens-Bogdanov point is considered as an isolated organizing centre. Two branches of symmetry-breaking and asymmetric Hopf bifurcation points as well as one branch of Z 2 -pitchforks which emanate from the organizing centre are analyzed via asymptotic expansions. Leading terms of these expansions are calculated explicitly. The input data are differentials (up to third order) of the mapping evaluated at the organizing centre along specified directions
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