The Pentagram map in higher dimensions and KdV flows
Dynamical Systems
2012-05-17 v1 Symplectic Geometry
Exactly Solvable and Integrable Systems
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 is shown to be the -flow of the KdV hierarchy, generalizing the Boussinesq equation in 2D.
Cite
@article{arxiv.1205.3744,
title = {The Pentagram map in higher dimensions and KdV flows},
author = {Boris Khesin and Fedor Soloviev},
journal= {arXiv preprint arXiv:1205.3744},
year = {2012}
}
Comments
11 pages, 3 figures; This note is a short announcement of arXiv:1204.0756