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- W4287758105 abstract "The pentagram map takes a planar polygon $P$ to a polygon $P'$ whose vertices are the intersection points of consecutive shortest diagonals of $P$. The orbit of a convex polygon under this map is a sequence of polygons which 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." @default.
- W4287758105 created "2022-07-26" @default.
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- W4287758105 date "2020-06-12" @default.
- W4287758105 modified "2023-09-29" @default.
- W4287758105 title "The limit point of the pentagram map and infinitesimal monodromy" @default.
- W4287758105 doi "https://doi.org/10.48550/arxiv.2006.07413" @default.
- W4287758105 hasPublicationYear "2020" @default.
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