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The studies developed in this work are concerned with the analysis of the effect of symmetry in steady-state bifurcation problems. Lie groups and singularity theory are used to analyse bifurcation problems on C with the action of the dihedral group D_n, n ≥ 3, n ≠ 4. The aim is to obtain results on the local behavior of such problems. Normal forms and unfolding for two generic D₃-equivariant problems are studies and the results are applied in the traction problem for deformation of an elastic cube (Mooney-Rivlin Material). An interesting example showing the global dynamic of a D₅-equivariant bifurcation problem is worked out.