Do ergodic or chaotic properties of the reflection law imply ergodicity or chaotic behavior of a particle's motion? (Q1893443)

The authors consider the motion of a particle confined to a region of the two-dimensional plane and subject to a certain reflection law at its boundary. It is their goal to show, by way of example, that properties of the particle motion such as ergodicity, chaotic behavior and periodicity cannot be directly read off from the reflection law. To that end they present numerical studies of a particle confined to a spherical region and to a quadratic region.