The pentagram map in higher dimensions and KDV flows

Abstract

We extend the definition of the pentagram map from 2D to higher dimensions and describe its integrability properties for both closed and twisted polygons by presenting its Lax form. The corresponding continuous limit of the pentagram map in dimension d is shown to be the (2,d + 1)-equation of the KdV hierarchy, generalizing the Boussinesq equation in 2D. © 2012 American Institute of Mathematical Sciences.