The pentagram zoo

Schwartz’s pentagram map is a dynamical system defined on moduli spaces of polygons by intersecting diagonals. It is an integrable system, meaning that in appropriate coordinates, the map becomes a family of translations on complex tori. Some natural generalizations of the pentagram map produce integrable systems, but numerical experiments by Khesin-Soloviev suggest that others do not. In this talk, we use tools from dynamical systems to prove that the “skew” pentagram map is non-integrable.