|XXVIII Workshop on Geometric Methods in Physics||28.06-04.07.2009|
The Pentagram map, a completely integrable system
Introduced by R. Schwartz 16 years ago, the pentagram map acts on non-degenerate plane n-gons, considered up to projective equivalence, by drawing the diagonals that connect second-nearest vertices and taking the new n-gon formed by their intersections. Based on a joint work with V. Ovsienko and R. Schwartz, I shall demonstrate that the pentagram map is completely integrable. I shall also explain that the pentagram map is a discretization of a well known completely integrable system, the Boussinesq equation.