Senior Honors Thesis Presentation: "Diffusion and Topology in Mixed Boundary Polygonal Billiard Systems"

Abstract: A billiard system represents the movement of point-particles inside a closed container. The shape and properties of such a container, or 'billiard table,' completely determine the system's properties. Consequently, billiard systems are often labeled by the shape of the billiard table, as such is the case with polygonal billiards. This thesis serves to generalize diffusion and topological results of classically defined polygonal billiards to a new system: mixed boundary polygonal billiards. Key results from this generalization include the presence of 'ballistic fronts' and the construction of the phase space of the billiard system— a 3-manifold foliated by the unfolded flat surfaces.

Host: Renato Feres