The Curious Link Chain

Abstract

First some strange example will be presented that shows what curious things may occur, when you deal with bifurcation under the presence of some symmetry group. In a second part it will be shown that such behavior is impossible for analytic bifurcation equations. Indeed, in this case the solution set near the bifurcation point can be decomposed into finitely many cells of (possibly) different dimension but constant symmetry. As a consequence, every solution sufficiently near to the bifurcation point can be joined to this point by an analytic curve of solutions all having the same symmetry except for the bifurcation point.