On classification of degenerate singular points of Ricci flows
Keywords:
Riemannian invariant metric, Einstein metric, generalized Wallach space, Ricci flow, dynamical system, system of nonlinear ordinary differential equations, singular point, degenerate singular point, parametric bifurcationsAbstract
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 ai = аj , i, j E{1, 2,3}, i<>j . In general the problem can also be considered as twoparametric bifurcations of solutions of abstract dynamical systems. Thus the problem under investigation is interesting not only in geometrical sense, but concerns the theory of planar dynamical systems.
