This thesis deals with steady-state mode interaction problems with symmetry.\ud We prove several results concerning problems invariant under the action of an\ud arbitrary compact Lie group Γ. These include the existence of mixed-mode\ud solutions and secondary Hopf bifurcations. We also consider the unfolding of\ud the equations characterizing such problems. Where appropriate, we distinguish\ud the case when Γ acts trivially on one of the modes. We then apply the results to\ud the problems of the (1,3)-, (1,5)- and (1,3,5)-mode interactions with spherical\ud symmetry. We also consider the (3,5)- and the (1,3,5)-mode interaction\ud problems with SO(3) symmetry
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