Lara Braverman, Harvard University

Dynamical Billiards on the surface of tilted cones

Crystals often grow on 3d surfaces embedded in 2d. The curvature of the surface effects the formation of crystalline structures and the interaction between defects causing grain boundaries as well as other patterns of disclinations and dislocations. Hence, statistical mechanical properties such as ergodicity of dynamical systems on 2d surfaces with varying boundaries are of interest. Here, we extend the well studied dynamical billiard problem with boundaries in 2d onto curved surfaces by placing it on flat surfaces with a conical singularity. It is well-known that a dynamical billiard system on a table with a circular boundary is integrable. In this poster, we demonstrate that either adding curvature or breaking azimuthal symmetry, by setting an elliptical boundary, alone is not sufficient to achieve chaos. However, the addition of both of these changes is. Surprisingly, in this novel chaotic system, unlike in previously studied systems, we observe that chaos can be achieved even with smooth convex boundary conditions. In addition, we also observe more common properties of chaos such as intermittent chaos in our system.