The set of invariant measures M(f) is a convex compact set in the weak topology. Extreme points of \(M(f)\) \(M(f)\) correspond to ergodic measures, The set \(M(G)\) of flows on the symbolic image is convex and simple flows are the extreme points of this set. It is shown that simple flows approximate ergodic measures. The relationship between supports of invariant measure and flows is also studied.