As an example, the figure presented here (left part) depicts the Poincaré section obtained when one applies periodically a figure-eight-like movement to a circular mixing rod. Some trajectories span a large region: this is the chaotic or mixing region, where good mixing occurs. However, there are also two "holes": in these regions, the trajectories are closed. These are called elliptic islands, as the trajectories inside are elliptic-like curves. These regions are not mixed with the remainder of the fluid. For mixing applications, elliptic islands have to be avoided for two reasons :
