Poincaré section

A surface (or "space") of section, also called a Poincaré section (Rasband 1990, pp. 7 and 93-94), is a way of presenting a trajectory in n-dimensional phase space in an (n - 1)-dimensional space. By picking one phase element constant and plotting the values of the other elements each time the selected element has the desired value, an intersection surface is obtained. The above surface of section is for the Hénon-Heiles equation with energy E = 1/8 plotting y(t) vs. y^.(t) at values where x(t) = 0.

Hénon-Heiles equation | phase portrait | phase space | Poincaré map