Abstract Important features can be totally obscured in such a diagram, but Poincare maps can be used to detect underlying structure, such as periodic solutions having the forcing or a subharmonic frequency. In this context the investigation of periodic solutions, nearly periodic solutions, and similar phenomena is to a considerable extent an exploratory matter in which computation plays at the present time a very significant part. A search for hidden periodicities, such as subharmonic periods, is best carried out by starting with a period in mind and then looking for solutions with this period. In that case a variant of the Poincare map is usually more profitable-if the solutions sought have period T, then we should plot on the x, y plane (if two dimensions are being considered) a sequence of points calculated at times T, 2T, 3T, ... along the phase paths starting from various states, and sec whether any of these sequences indicate that we are approaching a periodic solution. However, this does not quite fit the definition of a Poincare map, which does not involve any mention of time intervals but picks out intersections of a phase path under investigation with another given curve (the section’). The two procedures can with advantage for the analysis (especially in multidimensional cases) be brought together in a manner suggested by the following example.