Karin Gatermann

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This paper investigates generic bifurcations from a D m-invariant equilibrium of a D m-symmetric dynamical system, for m = 3 or 4, near points of codimension-2 steady-state mode interactions. The center manifold is isomorphic to IR 3 or IR 4 and is non-irreducible. Depending on the group representation, in the unfolding of the linearization we nd:(More)
The results from Invariant Theory and the results for semi-invariants and equivariants are summarized in a suitable way for combining with Grr obner basis computation. An algorithm for the determination of fundamental equivariants using projections and a Poincar e series is described. Secondly, an algorithm is given for the representation of an equiva-riant(More)
In two-parameter systems with symmetry two steady state bifurcation points of diierent symmetry types coalesce generically within one point. Under certain group theoretic conditions involving the action of the symmetry group on the kernels, we show that secondary Hopf bifurcation is borne by the mode interaction. We explain this phenomenon by using linear(More)