Isolating blocks for Morse flows
The qualitative description of the dynamical behavior of a continuous flow is generally divided in two parts: the ''gradient-like'' behavior which is reflected in the existence of a Lyapunov function, and the ''chain recurrent'' behavior. In order to study a class of dynamical systems it is important to understand two things: the first one is, for each of these two parts what kinds of behavior are possible, and the second one is how these two aspects of dynamical behavior interact. With this objective, Franks introduced Lyapunov graphs.
In this context, by using abstract Lyapunov graphs labelled with dynamical and homological abstract information, we present a constructive general procedure to build Morse flows on isolating blocks respecting given dynamical and homological boundary data recorded in abstract Lyapunov graphs.