Healy, LiamDeprit, EtienneGiven an integrable dynamical system with one degree of freedom, "painting" the integral over phase space proves to be a powerful technique for uncovering both global and local behavior. This graphical technique avoids numerical integration, employing instead a nonlinear method of assigning contrasting colors to the energy values to distinguish subtle details of the flow.en-USHamiltonianintegrabledynamicsphase flowvisualizationparallel computingcontour mapArticle