The University of Arizona
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The Pentagram map and infinitesimal monodromy

Hamiltonian Systems

The Pentagram map and infinitesimal monodromy
Series: Hamiltonian Systems
Location: ONLINE
Presenter: Quinton Aboud, University of Arizona

The pentagram map takes a planar polygon P to a polygon P' whose vertices are the intersection points of the consecutive shortest diagonals of P. The orbit of a convex polygon under this map is a sequence of polygons that converges exponentially to a point. Furthermore, as recently proved by Glick, coordinates of that limit point can be computed as an eigenvector of a certain operator associated with the polygon. In the talk, we will show that Glick’s operator can be interpreted as the infinitesimal monodromy of the polygon. Namely, there exists a certain natural infinitesimal perturbation of a polygon, which is again a polygon but in general not closed; what Glick’s operator measures is the extent to which this perturbed polygon does not close up.

The talk will be via Zoom at:

Passcode: 448487