The dynamics of the Ricci flow on generalized Wallach spaces

We consider the asymptotic behavior of the normalized Ricci flow on generalized Wallach spaces that could be considered as a special planar dynamical system. All non-symmetric generalized Wallach spaces can be naturally parameterized by three positive numbers a1a1, a2a2, a3a3. Our interest is to determine the type of singularity of all singular points of the normalized Ricci flow on all such spaces. Our main result gives a qualitative answer for almost all points (a1,a2,a3)(a1,a2,a3) in the cube (0,1/2]×(0,1/2]×(0,1/2](0,1/2]×(0,1/2]×(0,1/2].