On classification of degenerate singular points of Ricci flows

Abstract

We consider the normalized Ricci flow on generalized Wallach spaces that could be reduced to a system of nonlinear ODEs. As a main result we get the classification of degenerate singular points of the system under consideration in the important partial case a . In general the problem can also be considered as two-parametric bifurcations of solutions of abstract dynamical systems. Thus the problem un-der investigation is interesting not only in geometrical sense, but concerns the theory of planar dynamical sys-tems.