Computational Methods for Bifurcation Problems with Symmetries on the Manifold

摘要

This paper is about numerical methods for the determination of bifurcation pointsof certain steady state multi-parameter problems in the presence of symmetries. A principal tool is the fact that under general conditions the solution set forms a manifold in the space of all state and parameter variables. The reduced manifold with respect to some subsymmetry is introduced. Methods are presented for the local computation of the submanifold of bifurcation points of the same symmetry.