On topological structure of some sets related to the normalized Ricci flow on generalized Wallach spaces

Abstract

We study topological structures of the sets (0,1/2)3∩Ω and (0,1/2)3∖Ω, where Ω is one special algebraic surface defined by a symmetric polynomial of degree 12. These problems arise in studying of general properties of degenerate singular points of dynamical systems obtained from the~normalized Ricci flow on generalized Wallach spaces. Our main goal is to prove the connectedness of (0,1/2)3∩Ω and to determine the number of connected components of (0,1/2)3∖Ω.