Minimal Flows on Compact Manifolds

In this paper we compute the minimal number of non-degenerate singularities that can be realized on some manifold with non-empty boundary in terms only of abstract homological boundary information. We specify the index and the types (connecting or disconnecting) of the singularities realizing the minimum. The Euler characteristics of manifolds realizing the minimum are obtained and the associated Lyapunov graphs of Morse type are described and shown to have the lowest topological complexity.