Integrability and non-integrability of pentagram maps
by
Prof.Boris KHESIN(University of Toronto & IHÉS)
→
Europe/Paris
Amphithéâtre Léon Motchane (IHES)
Amphithéâtre Léon Motchane
IHES
Le Bois Marie
35, route de Chartres
91440 Bures-sur-Yvette
Description
We define pentagram maps on polygons in any dimension, which extend R. Schwartz's definition of the 2D pentagram map, as well as describe recent results on integrable cases for these higher-dimensional generalizations. The corresponding continuous limits of such maps coincide with equations of the KdV hierarchy, generalizing the Boussinesq equation in 2D. We discuss their geometry and a numerical evidence of non-integrability of certain cases. This is a joint work with Fedor Soloviev (Univ. of Toronto).