Anything that happens in a flow also happens in a (lower-dimensional) discrete dynamical system (and conversely).``The creed is stated in the mode of the sunshine patriot, leaving plenty of room to duck as necessary [3].'' This creed is implicit in Poincaré's original work, but was first clearly enunciated by Smale.
The essence of dynamical systems studies is stated in ``The Dynamical Quest'':
Where do orbits go, and what do they do/see when they get there?The dynamical quest emphasizes the topological (i.e., qualitative) characterization of the long-term behavior of a dynamical system.