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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)
«nitted in any form or by any means, ir any information storage and retrieval owner. 5e of an article in this journal indicates V be made for personal or internal use, is consent is given on the condition! i the Copyright Clearance Center, Ina ing beyond that permitted by Sections not extend to other kinds of copying, >r promotional purposes, for creating(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)