@misc{GatermannWerner, author = {Gatermann, Karin and Werner, Bodo}, title = {Group Theoretical Mode Interactions with Different Symmetries.}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-994}, number = {SC-93-03}, abstract = {In two-parameter systems two symmetry breaking bifurcation points of different types coalesce generically within one point. This causes secondary bifurcation points to exist. The aim of this paper is to understand this phenomenon with group theory and the innerconnectivity of irreducible representations of supergroup and subgroups. Colored pictures of examples are included.}, language = {en} } @misc{GatermannWerner, author = {Gatermann, Karin and Werner, Bodo}, title = {Secondary Hopf Bifurcation Caused by Steady-State Steady-State Mode Interaction.}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-1122}, number = {SC-93-16}, abstract = {In two-parameter systems with symmetry two steady state bifurcation points of different 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 representation theory. For motivation an example with \$D_3\$-symmetry is investigated where the main properties causing the Hopf bifurcation are summarized.}, language = {en} }