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- W2953980366 abstract "The pentagram map takes a planar polygon $P$ to a polygon $P'$ whose vertices are the intersection points of consecutive shortest diagonals of $P$. This map is known to interact nicely with Poncelet polygons, i.e. polygons which are simultaneously inscribed in a conic and circumscribed about a conic. A theorem of R. Schwartz says that if $P$ is a Poncelet polygon, then the image of $P$ under the pentagram map is projectively equivalent to $P$. In the present paper we show that in the convex case this property characterizes Poncelet polygons: if a convex polygon is projectively equivalent to its pentagram image, then it is Poncelet. The proof is based on the theory of commuting difference operators, as well as on properties of real elliptic curves and theta functions." @default.
- W2953980366 created "2019-07-12" @default.
- W2953980366 creator A5054674786 @default.
- W2953980366 date "2019-06-25" @default.
- W2953980366 modified "2023-09-27" @default.
- W2953980366 title "The pentagram map, Poncelet polygons, and commuting difference operators" @default.
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