Abstract
Translation and reflection symmetries introduce the group 0(2) into bifurcation problems with periodic boundary conditions. The effect on the Hopf bifurcation with 0(2)-symmetry of small terms breaking the translation symmetry is investigated. Two primary branches of standing waves are found. Secondary and tertiary bifurcations involving two different types of modulated waves are analyzed in the neighborhood of secondary Takens-Bogdanov bifurcations. The effects of breaking the phaseshift (in time) and reflection symmetries are briefly considered.
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Dangelmayr, G., Knobloch, E. (1987). On the Hopf Bifurcation with Broken O(2) Symmetry. In: Güttinger, W., Dangelmayr, G. (eds) The Physics of Structure Formation. Springer Series in Synergetics, vol 37. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-73001-6_30
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DOI: https://doi.org/10.1007/978-3-642-73001-6_30
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