Periodic Paths on the Pentagon

by Diana Davis (Swarthmore College & IHES)

Thursday Mar 14, 2019, 10:30 AM → 11:30 AM Europe/Paris

Amphithéâtre Léon Motchane (IHES)

Mathematicians have long understood periodic trajectories on the square billiard table, which occur when the slope of the trajectory is rational. In this talk, I will explain my joint work with Samuel Lelièvre on periodic trajectories on the regular pentagon, describing their geometry, symbolic dynamics, and group structure. The periodic trajectories are very beautiful, and some of them exhibit a surprising "dense but not equidistributed" behavior.