The pentagram map, Poncelet polygons, and commuting difference operators

@article{Izosimov2019ThePM,
  title={The pentagram map, Poncelet polygons, and commuting difference operators},
  author={Anton Izosimov},
  journal={Compositio Mathematica},
  year={2019},
  volume={158},
  pages={1084 - 1124}
}
  • A. Izosimov
  • Published 25 June 2019
  • Mathematics
  • Compositio Mathematica
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, that is, polygons which are simultaneously inscribed in a conic and circumscribed about a conic. A theorem of Schwartz states 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… 

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