SYMMETRY-BREAKING BIFURCATIONS ON MULTIDIMENSIONAL FIXED-POINT SUBSPACES

Symmetry-breaking bifurcations associated with fixed point subspaces o f dimension greater than one are considered, for maximal isotropy subg roups, using techniques of blowing-up and degree theory. The leading n on-linear term in the Taylor expansion of the bifurcation mapping rest ricted to the fixed point subspace, when satisfying a certain traversa lity condition or the non-vanishing of an appropriate index, governs t he branching. Numerous primary symmetry-breaking branches are obtained and their stability is investigated. Applications involving gradient leading order terms have been calculated using Grobner bases and compu ter algebra. A general result on symmetty-breaking from O (3) is prese nted.