| Résume | The pentagram map on polygons in the projective plane was introduced
by R. Schwartz in 1992 and is by now one of the most popular and
classical discrete integrable systems. We survey definitions and
integrability properties of the pentagram maps on generic plane
polygons and their generalizations to higher dimensions. In
particular, we define long-diagonal pentagram maps on polygons in
RP^d, encompassing all known integrable cases. We also describe the
corresponding continuous limit of such pentagram maps: in dimension d
is turns out to be the (2, d + 1)-equation of the KdV hierarchy,
generalizing the Boussinesq equation in 2D. This is a joint work with
F.Soloviev and A.Izosimov. |
