O(2) equivariant mode interactions

This thesis uses and develops methods of equivariant bifurcation theory in the context of 0(2) equivariant steady-state and Hopf mode interactions in circumstances where both two and three modes interact. The general actions of the 0(2) orthogonal group are applied to these mode interactions and as an illustration the 0(2) equivariant steady-state/Hopf/Hopf mode interaction is placed in the context of the Taylor-Couette system.