(Qualitative) Dynamical Analysis

Stephen Smale was among the first to use the expression "dynamical system" to make it clear that he was paying attention to something other than the differential equations which described the system.

He thought about dynamical systems in terms of their geometry - the topology (shape/continuity) of their phase space trajectories - rather than the formulas used to define them.

This shift to paying attention to the shapes in phase space is a shift from a quantitative and local description of the system to a global and qualitative description.