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Steady-state mode interactions in the presence of O(2)-symmetry and in non-flux boundary value problems. (English) Zbl 0602.58039
Multiparameter bifurcation theory, Proc. AMS-IMS-SIAM Joint Summer Res. Conf., Arcata/Calif. 1985, Contemp. Math. 56, 53-68 (1986).
[For the entire collection see Zbl 0587.00009.]
The authors’ abstract seems to do justice to the paper and is reproduced below. ”This paper reviews recent results concerning the multiple bifurcation phenomenon of steady-state mode interactions in the presence of O(2)-symmetry and in non-flux boundary value problems. The normal forms for these two problems are closely related. In the generic case there are primary bifurcations from the basic state to single mode solutions, secondary bifurcations to mixed mode solutions and, in some instances, tertiary Hopf bifurcations to standing waves. The O(2)-problem can also encounter tertiary bifurcations to traveling or rotating waves. The qualitative type of the bifurcation diagrams depends on the wave numbers.”
Reviewer: P.N.Bajaj

MSC:
37G99 Local and nonlocal bifurcation theory for dynamical systems