An example of a chaotic trajectory is shown in Fig. 5. The trajectories that hit only the concave sides are stable and belong to the integrable regions, and trajectories that hit the convex sides are generally chaotic. Another observation which can be made is that the regular regions occupy less area than the chaotic sea and therefore the clover billiard is mainly chaotic. Beside the trajectories that generates the two main regular islands and the chaotic sea there are an infinite number of other stable and unstable trajectories present and some examples are shown in Figs. There are very few completely regular or chaotic systems in nature and most systems are the mixed systems.
Mixed systems are also more rich compared to the integrable and chaotic limits.
In our case we are studying the wave properties of systems with mixed classical phase space by measuring the acoustical eigenvalue spectrum of a clover shaped quartz plate.