Details

Autor(en) / Beteiligte

• Aboud, Quinton
• Izosimov, Anton

Titel

The Limit Point of the Pentagram Map and Infinitesimal Monodromy

Ist Teil von

• International mathematics research notices, 2022-03, Vol.2022 (7), p.5383-5397

Erscheinungsjahr

2022

Beschreibungen/Notizen

• Abstract The pentagram map takes a planar polygon $P$ to a polygon $P^{\prime }$ 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 present paper, we 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.