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  1. ; (, International Mathematics Research Notices)
    null (Ed.)
    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. 
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