Alternatives to the standard Poincare´ section are proposed to cater for some conditions arising in the study of chaotic ray propagation where the usual method of dimension reduction by the Poincare´ section is inadequate because the driving is notperiodic. There are three alternatives proposed which all use the same surface of intersection, but which differ in their use of the values of the dependent variables at the intersections of the rays with the surface. The new reduction techniques are used to examine ray behaviour in a harmonically perturbed Munk profile which supports raychaos. It is found that all three techniques provide a graphical means of distinguishing between regular and irregular motions, and that the space of the mapping associated with one of the mispartitioned in to non intersecting regular and chaotic regions as with the Poincare´ section. A further model with quasi periodic time dependence of the Hamiltonian is examined, and it turns out that the quasi periodic nature of the motion is revealed as Lissajous curves by one technique.
Bodai, T., Fenwick, A. J., & Wiercigroch, M. (2009). New graphical tools for studying acoustic ray propagation. Journal of Sound and Vibration, 324(3-5), 850–860. https://doi.org/10.1016/j.jsv.2009.01.049