Computability of Limit Sets for Two-Dimensional Flows

A classical theorem of Peixoto qualitatively characterizes, on the two-dimensional unit ball, the limit sets of structurally stable flows defined by ordinary differential equations. Peixoto's density theorem further shows that such flows are typical in the sense that structurally stable systems form an open dense set in the space of all continuously differentiable flows. In this note, we discuss the problem of explicitly finding the limit sets of structurally stable planar flows.